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in Physics by (64.7k points)

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. Will it reach the bottom with the same speed in each case? Will in take longer to roll down one plane than the other? If so, which one and why?

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Let v be the speed of the solid sphere at the bottom of incline.

Applying principle of conservation energy.

1/2 mv2 + 1/2 Iω2 = mgh

As I = 2/5 mR2;

As h is same in both the case v must be same, i.e., it will reach the bottom with the same speed for both the inclination. Time taken to roll down both the inclinations would be also the same, as their heights are equal.

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