A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane?

Step-by-step solution

Let the inclination of the inclined plane be . Acceleration of a rolling body is given as a= g (1+K^2 / R^2 ) Here, K is radius of gyration. For circular disc I= 1 2 M R^2 K^2 R^2 = 1 2 a= 2 3 g For solid cylinder I= 1 2 M R^2 K^2 R^2 = 1 2 a= 2 3 g For solid sphere I= 2 5 M R^2 K^2 R^2 = 2 5 a= 5 7 g For hollow cylinder I=M R^2 K^2 R^2 =1 a= 1 2 g Hence, from (i), (ii), (iii) and (iv) we conclude that the solid sphere will reach the bottom with maximum acceleration.