Question

A solid sphere, starting from rest, rolls down two different inclined planes from the same height but with different angles of inclination θ₁ > θ₂ . On which plane will the sphere take longer time to roll down?

Answer 1

Let L₁ and L₂ be the distances rolled down by the sphere along the corresponding inclines from the same height h. 

∴ L₁ sin θ₁ = L₂ sin θ₂ = h

Therefore,  h being the same, \(V_{CM1}\) = \(V_{CM2}\)

v = u + at

with u = 0 and  \(V_{CM1}\) = \(V_{CM2}\), a_CM1t₁ = a_CM2t_2.

The sphere will take longer time to roll down from the same height on the plane with smaller inclination.