Question

Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from the rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain.

Answer 1

In the figure above, we have two smooth planes tracks inclined to the horizontal at ∠θ₁ and ∠θ₂, respectively.

As height of both the tracks is the same, therefore, both the stones will reach the bottom with the same speed.

P.E. = K.E.

⇒ mgh = 1/2 mv₁² = 1/2 mv₂²

⇒ v₁ = v₂

From the Fig., acceleration of the two stones are:

a₁ = g sinθ₁ and a₂ = g sinθ₂

As θ₂ > θ₁, a₂ > a₁

From v = u + a = 0 + at

or, t = v/a

As t α 1/a and a₂ > a₁, t₂ < t₁

i.e., the second stone will take lesser time and reach the bottom earlier than the first stone.