JEE MAIN - Physics (2025 - 24th January Evening Shift - No. 20)
A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right)$ where $x_0=1 \mathrm{~m}$. The kinetic energy $(\mathrm{K})$ of the particle as a function of $x$ is correctly represented by the graph
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Explanation
$$\begin{aligned} & x=x_0 \sin ^2 \frac{t}{2}=x_0\left(\frac{1-\cos t}{2}\right) \\ & x-\frac{x_0}{2}=\frac{-\cos t}{2} \\ & \text { where } x_0=1 \\ & x-\frac{1}{2}=\frac{-\cos t}{2} \end{aligned}$$
Particle is oscillating between $\mathrm{x}=0$ to $\mathrm{x}=1$
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