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  • 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?

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?
(a) Both the stones reach the bottom at the same time but not with the same speed.
(b) Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.
(c) Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
(d) Both the stones reach the bottom at different times and with different speeds.

Answers (1)

The answer is the option (c) Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.

AB and AC are plains which inclined at angle \theta _{1} and \theta _{2}. Friction is absent as the plains are assumed to be smooth, which leads to the conservation of mechanical energy.

 

For both AB and AC,

\frac{1}{2} mv^{2} = mgh and

v= \sqrt{2gh}

Speed is the same for both stones.

Stone I

Acceleration

a_{1} = g \sin\theta_{1}

Stone II

Acceleration

a_{2} = g \sin\theta_{2}

Now, \theta_{2} >\theta_{1} and hence a_{2} >a_{1}. So, stone II reaches faster than stone I.

Posted by

infoexpert24

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