In the given arrangement of doubly | Friction|JEE-Main 2023

JEE MAINS 2024

31.01.24 S1

Question

In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25 . The value of $m$, for which $M=10 \mathrm{~kg}$ will move down with an acceleration of $2 \mathrm{~m} / \mathrm{s}^2$, is: (take $g=10 \mathrm{~m} / \mathrm{s}^2$ and $\left.\tan 37^{\circ}=3 / 4\right)$

Select the correct option:

9 kg

4.5 kg

6.5 kg

2.25 kg

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Sol. For M block| $$ \begin{aligned} & 10 \mathrm{~g} \sin 53^{\circ}-\mu(10 \mathrm{~g}) \cos 53^{\circ}-\mathrm{T}=10 \times 2 \\ & \mathrm{~T}=80-15-20 \\ & \mathrm{~T}=45 \mathrm{~N} \end{aligned} $$ For $m$ block $$ \mathrm{T}-\mathrm{mg} \sin 37^{\circ}-\mu \mathrm{mgcos} 37^{\circ}=\mathrm{m} \times 2 $$ $\begin{aligned} & 45=10 \mathrm{~m} \\ & \mathrm{~m}=4.5 \mathrm{~kg}\end{aligned}$

Question Tags

JEE Main

Physics

Medium

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