An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle (as shown in figure) between the direction of force and horizontal varies as = kx, where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be . The value of n is___.[
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Solution
Sol. $F \cos \theta=m a$
$$
\begin{aligned}
& 2 \cos (k x)=\frac{m v d v}{d x} \\
& \int_0^v v d v=2 \int_0^x \cos (k x) d x \\
& \frac{m v^2}{2}=\frac{2}{k} \sin k x \\
& \text { K.E. }=\frac{2}{k} \sin \theta \\
& n=2
\end{aligned}
$$
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