A small object of uniform density rolls up a curved surface with an initial velocity v . It reaches upto a maximum height of 7 v^2 10 g with respect to initial position. Then the object is

Step-by-step solution

By the conservation of energy, aligned & & E_i & =E_f & & 1 2 m v^2+ 1 2 l ^2 & =m g H=m g ( 7 v^2 10 g ) & & 1 2 m v^2+ 1 2 l v^2 R^2 & = 7 10 m v^2 ( v= R) & & 1 2 I v^2 R^2 & = ( 7 10 - 1 2 ) m v^2 & & & = 2 10 m v^2= 1 5 m v^2 & & I & = 2 5 m R^2 aligned The above value of moment of inertia is equal to moment of inertia of solid sphere.