A circular disc reaches from top to bottom of an inclined plane of length L . When it slips down the plane, it takes time t 1 . When it rolls down the plane, it takes time t 2 . The value of t 2 t 1 is 3 x . The value of x will be

Step-by-step solution

If disk slips on inclined plane, then its acceleration, a 1 = g sin θ L = 1 2 a 1 t 1 2 ⇒ t 1 = 2   L a 1   … i If disk rolls on inclined plane, its acceleration, a 2 = g sin θ 1 + I m R 2 a 2 = g sin θ 1 + m R 2 2   m R 2 a 2 = 2 3 g sin θ Now L = 1 2 a 2 · t 2 2 ⇒ t 2 = 2   L a 2   … ii Now, t 2 t 1 = a 1 a 2 = 3 2 ⇒ x = 2