A solid sphere, a hollow sphere and a disc, all having same mass and r

1.	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» (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=0t+½g.sinθt² t²=2S/g.sinθ t=√{2S/g.sinθ} where S is the length of the incline.

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»

(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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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.

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