Question

A body slides down an inclined plane in time ' t '.calculate the time taken by a ring to roll down the inclined plane without slipping.

Answer 1

Time taken by a body to slide down an inclined plane:

$t =\sqrt{\frac{2h}{gsin\theta } }$

Time taken by a body to roll down an inclined plane, where,

K= radius of gyration

R= radius

$t' =\sqrt{\frac{2h(1+\frac{K^{2} }{R^{2} }) }{gsin\theta } }$

for a ring, the ratio of K²/R² = 1

$t' =\sqrt{\frac{2h(1+1) }{gsin\theta } }\\\\t' = \sqrt{{2}}t$

Thus t' = √2 t is the required answer