A block 'A' takes 2 s to slide down a frictionless incline of 30 °… | JEE Main 2022 (27 Jul, Shift 2)

Q22JEE Main 2022 · 27 JUL · SHIFT 2Medium

Connected Bodies & Pulleys

A block 'A' takes 2 s to slide down a frictionless incline of 30 $^\circ$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to 45 $^\circ$ , the time taken by the block, to slide down the incline, will be approximately:

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Answer: (c)

A lift moving with uniform velocity is an inertial frame, so effective $g$ is unchanged.
On a frictionless incline: $l = \frac{1}{2}g\sin\theta\, t^2 \Rightarrow t \propto \dfrac{1}{\sqrt{\sin\theta}}$ .
$t' = 2\sqrt{\dfrac{\sin 30^\circ}{\sin 45^\circ}} = 2\sqrt{0.707} = 2 \times 0.84$
$t' \approx 1.68\text{ s}$ , so the answer is (c).

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