A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of a same incline and released.
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of a same incline and released. Least time will be taken reaching the bottom by
(a) the solid sphere
(b) the hollow sphere
(c) the disc
(d) all will take same
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(d) all will take same
Explanation:
Since there is no friction on the incline, the only force on each of these objects along the incline is their weight component mg.sinθ.
So each of them have same initial velocity=0 and same acceleration=mg.sinθ/m = g.sinθ
So the time taken by each of them t is given by
S=0*t+½g.sinθ*t²
t²=2S/g.sinθ
t=√{2S/g.sinθ}
where S is the length of the incline.
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