A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30 ° , then and the angle of inclination of plane B must be (approximately).

Step-by-step solution

The hollow cylinder and sphere both are rolling down without slipping therefore the acceleration down the inclined plane for both is, a cylinder = g sin θ 1 + I cylinder m r 2   and a sphere = g sin 30 ° 1 + I sphere m r 2   For time taken to reach the bottom surface, s = u t + 1 2 a t 2 s = 1 2 a t 2 ⇒ t = 2 s a ⇒ t = 2 s g sin θ 1 + I m r 2 = 2 s m r 2 + I m r 2 g sin θ For sphere moment of inertia is, I spere = 2 5 m r 2   therefore, t ' = 2 s m r 2 + I m r 2 g