A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Time taken by the body to reach the bottom when it rolls down on an inclined plane without slipping is given byt=2l1+k2R2gsinθ Since g is constant and l,R and sinθ are same for both ∴tdts=1+kd2R21+ks2R2=1+R22R21+2R25R2∵kd=R2,ks=25R=32×57=1514⇒td>ts Hence, the sphere gets to the bottom first.