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 statements is correct?
Text Solution
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: In figure, AB and AC are two smooth planes inclined to the horizontal at 
respectively.
As height of both the planes in the same, therefore, both the stones will reach the bottom with same speed.
According to law of conservation of mechanical energy,
PE at the top = KE at the bottom
……(i)
And mgh 
……(ii)
From (i) and (ii), we get 
As is clear from figure, acceleration of the two stones are
respectively.
As 
From v = u +at = 0 
As 
and 
Hence, stone II will take lesser time and reach the bottom earlier than stone I.
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