An object of uniform density rolls up the curved path with the initial velocity v₀ as shown in the figure. If the maximum height attained by an object is 7v₀^2 10g ( g = acceleration due to gravity), the object is a _______.

Step-by-step solution

By the law of conservation of mechanical energy, the total initial kinetic energy of the rolling object is converted into potential energy at the maximum height. Total initial kinetic energy for an object rolling without slipping is given by: K = K_ translational + K_ rotational K = 1 2 mv₀^2 + 1 2 I ^2 Substituting = v₀ R and I = mk^2 (where k is the radius of gyration): K = 1 2 mv₀^2 + 1 2 (mk^2) ( v₀ R )^2 = 1 2 mv₀^2 (1 + k^2 R^2 ) The potential energy at the maximum height h is: U = mgh Given h = 7v₀^2 10g , w