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Question
Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in figure.
Which of the following statement is correct?
Options
Both the stones reach the bottom at the same time but not with the same speed.
Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.
Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
Both the stones reach the bottom at different times and with different speeds.
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Solution
Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
Explanation:
As seen in the diagrams, AB and AC are two smooth planes inclined at the angles θ1 and θ2, respectively.
Because there is no friction here, mechanical energy will be preserved.
Because both tracks have the same height h,
`1/2 mv^2 = mg`
`hv = sqrt(2gh)`
Hence, speed is the same for both stones. For stone I, a1 = acceleration along the inclined plane = g sin θ1
Similarly, for stone II, a2 = g sin θ2
And because track II is shorter in length, stone II arrives earlier than stone I.
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