Q JEE MAIN 2024

A disc of radius and mass is rolling horizontally without slipping with speed . It then moves up an inclined...

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Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length...

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A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from...

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Two circular dises of radius each 10 cm are joined at their centres by a rod of length 30 cm...

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A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to $I_1$....

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A thin uniform rod $(\mathrm{X})$ of mass M and length L is pivoted at a height $\left(\frac{L}{3}\right)$ as shown in...

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Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy...

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Suppose there is a uniform circular disc of mass Mkg and radius rm shown in figure. The shaded regions are...

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The moment of inertia of a square loop made of four uniform solid cylinders, each having radius $R$ and length...

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A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$...

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Two masses $m$ and 2 m are connected by a light string going over a pulley (disc) of mass 30...

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A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses...

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Q JEE MAIN 2026

Two identical thin rods of mass $M \mathrm{~kg}$ and length $L \mathrm{~m}$ are connected as shown in figure. Moment of...

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A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of...

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A uniform rod of mass $m$ and length $l$ suspended by means of two identical inextensible light strings as shown...

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Q JEE MAIN 2026

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of...

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Two cars A and B each of mass $10^3$kg are moving on parallel tracks separated by a distance of 10...

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Q JEE MAIN 2020

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a...

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Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings...

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Q JEE-MAIN 2019

The increasing order of reactivity of the following compounds towards reaction with alkyl halides directly is

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The molecule that has minimum/no role in the formation of photochemical smog, is

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Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius...

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Q JEE MAIN 2019

A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle...

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A thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma(r)=k r^2$ where $r$ is the...

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Q JEE MAIN 2020

A force $\vec{F}=(\hat{i}+2 \hat{j}+3 \hat{k}) \mathrm{N}$ acts at a point $(4 \hat{i}+3 \hat{j}+\hat{k}) \mathrm{m}$. Then the magnitude of torque about...

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Q JEE MAIN 2019

The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of...

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Q JEE MAIN _2019_

A particle of mass $m$ is moving along a trajectory given by $$ \begin{aligned} & x=x_0+a \cos \omega_1 t \\...

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Q JEE MAIN 2020

The linear mass density of a thin rod $A B$ of length $L$ varies from $A$ to $B$ as $$...

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Q JEE MAIN 2020

Four point masses, each of mass m , are fixed at the corners of a square of side $\ell$. The...

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Q JEE MAIN_2021_

Two coaxial discs, having moments of inertia $I_1$ and $\frac{1}{2}$, are rotating with respective angular velocities $\omega_1$ and $\frac{\omega_1}{2}$ about...

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Q JEE MAIN 2020

Shown in the figure is a hollow icecream cone (it open at the top). If its mass is M, radius...

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Q JEE MAIN 2020

Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres...

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A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that...

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Consider a uniform rod of mass $M=4 m$ and length I pivoted about its centre. A mass $m$ moving with...

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An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are...

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A wheel is rotating freely with an angular speed  on a shaft. The moment of inertia of the wheel...

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A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a...

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A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal...

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Q JEE MAIN 2020

A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_1$. If another...

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Q JEE MAIN 2019

A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible...

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ABC is a plane lamina of the shape of an equilateral triangle. $\mathrm{D}, \mathrm{E}$ are mid points of $\mathrm{AB}, \mathrm{AC}$...

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To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force...

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Q JEE MAIN 2019

A circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same...

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Q JEE MAIN 2019

The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force...

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Q JEE MAIN 2019

A rod of length 50 cm is pivoted at one end. It is raised such that it makes an angle...

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Q JEE MAIN 2020

Consider two uniform discs of the same thickness and different radii $R_1=R$ and $R_2=\alpha R$ made of the same material....

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A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is...

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Q JEE-MAIN 2020

An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass $m$ situated at...

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Q JEE-MAIN 2020

A uniform rod of length ' $l$ ' is pivoted at one of its ends on a vertical shaft of...

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For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to...

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Q JEE MAIN 2019

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic...

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A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at...

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Q JEE MAIN 2020

As shown in the figure, a bob of mass m is tied by a massless string whose other end portion...

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Q JEE MAIN 2019

Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at rest....

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A thin smooth rod of length L and mass M is rotating freely with angular speed 0 about an axis...

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The radius of gyration of a uniform rod of length I, about an axis passing through a point $\frac{1}{4}$ away...

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Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of...

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A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The...

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Q JEE MAIN 2021

Angular momentum of a single particle moving with constant speed along circular path

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Match List-I with List-II

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A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of...

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A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of...

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Two discs have moments of intertia $l_1$ and $l_2$ about their respective axes perpendicular to the plane and passing through...

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Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular...

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A thin circular plate of mass $M$ and radius $R$ has its density varying as $\rho(r)=\rho_0 r$ with $\rho_0$ as...

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The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of...

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In the given figure, two wheels P and Q are connected by a belt B. The radius of P is...

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A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and...

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A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm...

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A particle of mass ' $m$ ' is moving in time ' $t$ ' on a trajectory given by $$...

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The centre of a wheel rolling on a plane surface moves with a speed $v_0$. A particle on the rim...

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A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm'...

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Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R....

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A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the...

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Q JEE MAIN 2021

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined...

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Q JEE MAIN 2021

A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and...

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Q JEE MAIN 2019

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both...

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The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for...

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Q JEE MAIN 2021

Choose the correct answer from the options given below :

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A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of...

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Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The...

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Q JEE MAIN 2021

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic...

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A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the...

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A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined...

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Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia...

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Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $I$. The...

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A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of $1 \mathrm{~ms}^{-1}$ goes...

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Q JEE MAIN 2021

A solid disc of radius ' $a$ ' and mass ' $m$ ' rolls down without slipping on an inclined...

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Q JEE MAIN 2021

s $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. It starts from rest and was at the origin initially. After 4s, its new...

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Q JEE MAIN 2021

A force $\vec{F}-=4 \hat{i}+3 \hat{j}+4 \hat{k}$ is applied on an intersection point of $x=2$ plane and $x$-axis. The magnitude of...

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Q JEE_MAIN_2021

The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass...

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Q JEE_MAIN_2021

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of...

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A mass M hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass...

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A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$....

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A triangular plate is shown. A force $=\vec{F}=4 \hat{i}-3 \hat{j}$ is applied at point P . The torque at point...

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Q JEE MAIN 2021

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is...

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Four equal masses, m each are placed at the corners of a square of length (l) as shown in the...

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Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners...

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A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and...

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A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The...

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A uniform disc with mass $M=4 \mathrm{~kg}$ and radius $R=10 \mathrm{~cm}$ is mounted on a fixed horizontal axle as shown...

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Q MEMORY BASED QUESTION 2026

A rod of mass $m$ and length l is attached to two ideal strings. Find tension in left string just...

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The torque of a force $5 \hat{i}+3 \hat{j}-7 \hat{k}$ about the origin is $\tau$. If the force acts on a...

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Four identical discs each of mass ' $M$ ' and diameter ' $a$ ' are arranged in a small plane...

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The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through...

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A pulley of radius 1.5 m is rotated about its axis by a force $\mathrm{F}=\left(12 \mathrm{t}-3 \mathrm{t}^2\right) \mathrm{N}$ applied tangentially...

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Q JEE MAIN 2022

A disc of mass 1 kg and radius R is free of rotate about a horizontal axis passing through its...

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A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane...

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A $\sqrt{34} \mathrm{~m}$ long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3...

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Q JEE MAIN 2022

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is $\mathrm{l}_{1 .}$....

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Moment of Inertia (M.I.) of four bodies having same mass ‘M’ and radius ‘2R’ are as follows: I1= M.I. of...

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Solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational...

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The position vector of 1 kg object is $\vec{r}=(3 \hat{i}-\hat{j}) \mathrm{m}$ and its velocity $\vec{v}=(3 \hat{j}+k) \mathrm{ms}^{-1}$. The magnitude of...

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A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g...

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A body of mass 5 kg moving with a uniform speed $3 \sqrt{2} \mathrm{~ms}^{-1}$ in $X-Y$ plane along the line...

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A spherical shell of 1 kg mass and radius $R$ is rolling with angular speed $\omega$ on horizontal plane (as...

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A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 $\mathrm{rads}^{-1}$ in...

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Q JEE MAIN 2024

A uniform rod AB of mass 2 kg and Length 30 cm at rest on a smooth horizontal surface. An...

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Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light...

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A body of mass ' $m$ ' is projected with a speed ' $u$ ' making an angle of $45^{\circ}$...

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A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii...

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Q JEE MAIN 2024

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving...

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Two discs of moment of inertia $I_1=4 \mathrm{~kg} \mathrm{~m}^2$ and $\mathrm{I}_2=2 \mathrm{~kg} \mathrm{~m}^2$ about their central axes \& normal to...

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Q JEE MAIN 2024

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on...

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If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then...

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A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The...

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Q JEE MAIN 2025

A solid sphere with uniform density and radius R is rotating initially with constant angular velocity $\left(\omega_1\right)$ about its diameter....

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A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm ....

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A rod of linear mass density ' $\lambda$ ' and length ' $L$ ' is bent to form a ring...

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Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its...

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$M$ and $R$ be the mass and radius of a disc. A small disc of radius $R / 3$ is...

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A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim...

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A force of $-P \hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is...

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A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is...

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A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown...

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m/s at t = 0...

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Q JEE MAIN 2023

Match List I with List II. Choose the correct answer from the options given below :

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A particle of mass 100 g is projected at time $\mathrm{t}=0$ with a speed $20 \mathrm{~ms}^{-1}$ at an angle $45^{\circ}$...

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Q JEE MAIN 2023

Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm...

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Moment of inertia of a dise of mass $M$ and radius ' $R$ ' about any of its diameter is...

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Q JEE MAIN_2023

A uniform solid cylinder with radius R and length L has moment of inertia I1, about the axis of cylinder....

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Q JEE MAIN 2023

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of...

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A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping....

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For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of...

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A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0,...

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A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular...

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Q JEE MAIN 2023

The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of...

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Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a...

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A thin uniform rod of length 2 m . cross sectional area ' $A$ ' and density ' d '...

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ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to...

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A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60...

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A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J...

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A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is $...

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Q JEE MAINS 2024

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg...

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Q JEE MAINS 2024

A solid circular disc of mass 50" " kg rolls along a horizontal floor so that its center of mass...

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If the radius of earth is reduced to three-fourth of its present value without change in its mass then value...

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Q JEE MAIN 2024

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v...

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Q JEE MAIN 2024

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment...

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Consider a Disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10rad/s about an axis perpendicular...

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Q JEE MAIN 2024

A cylinder is rolling down on an inclined plane of inclination $60^{\circ}$. It's acceleration during rolling down will be $...

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Q JEE MAIN 2025

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim...

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Q JEE MAIN 2025

The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in...

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Q JEE MAIN 2024

Four particles each of mass 1kg are placed at four corners of a square of side 2 m. Moment of...

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Q JEE MAIN 2025

Three equal masses $m$ are kept at vertices ( $\mathrm{A}, \mathrm{B}, \mathrm{C}$ ) of an equilateral triangle of side $a$...

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Q JEE MAIN 2025

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping....

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Q JEE MAIN 2025

Which of the following are correct expression for torque acting on a body? A. $...

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Q JEE MAIN 2025

If $\vec L$ and $\vec P$ represent the angular momentum and linear momentum respectively of a particle of mass '$m$'...

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Q JEE MAIN 2025

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg ,...

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A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm...

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Q JEE MAIN 2025

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the...

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Q JEE MAIN 2025

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined...

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Q JEE MAIN 2025

A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are...

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Q JEE MAIN 2025

Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and...

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Q JEE MAIN 2025

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The...

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A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure....

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Q JEE MAIN 2025

The coordinates of a particle with respect to origin in a given reference frame is (1,1,1) meters. If a force...

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Two iron solid discs of negligible thickness have radii ${R_1}$ and ${R_2}$ and moment of intertia ${I_1}$ and ${I_2}$, respectively....

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Q JEE MAIN 2025

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of...

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An object of mass 'm' is projected from origin in a vertical xy plane at an angle ${45^0}$ with the...

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Q JEE MAIN 2025

A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination $45º$. If...

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Q JEE MAIN 2025

A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from...

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Q JEE MAIN 2025

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk....

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Q JEE MAIN 2025

The position vectors of two 1 kg particles, (A) and (B), are given by $\overrightarrow{\mathbf{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \hat{j}+\alpha_3 \hat{t}\right) \mathrm{m}$...

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Q JEE MAIN 2025

A uniform circular disc of radius 'R' and mass 'M' is rotating about an axis perpendicular to its plane and...

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Q JEE MAIN 2025

The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is...

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