Question

A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of a smooth incline and released. Least time will be taken in reaching the bottom by

(a) the solid sphere
(b) the hollow sphere
(c) the disc
(d) all will take same time.

Answer 1

Answer ⇒ Option (d)


Explanation ⇒ According to the question, there is no friction on the incline, as a result the only force on each of these objects along the incline is their component of the weight (or Force of the Gravity) which will be given by the Relation,
F = mg.sinθ.

Acceleration = Force/Mass
∴ a = mg.sinθ/m
⇒ a = g Sinθ

Since, each of them have same initial velocity = 0
and have the same acceleration of g Sin θ.

∴ For the time, using the Galileo's second equation of the motion,
S = ut + 1/2 × at²
S = 0 × t + 1/2 × g × sinθ*t²
t² = 2S/g × sinθ
t = $\sqrt{\frac{2S}{g.sin\theta}}$

Since, there must be some magnitude. Therefore, Option (d). is Correct.


Hope it helps.