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Q.

A trough has two identical inclined segments and a horizontal segment. A ball is released on the top of one inclined part and it oscillates inside the trough. Friction is large enough to prevent slipping of the ball. Time period of oscillation is T. Now the liner dimension of each part of the trough is enlarged four times. Find the new time period of oscillation of the ball.

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a

T

b

2T

c

T/2

d

T/3

answer is B.

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Detailed Solution

Let acceleration on inclined part (while going up as well as while going down) be a. Length of inclined part be $l_{1}$ and that of flat part be $l_{2}$ .
Total time period is given as
$[\sqrt{\frac{2 l_{1}}{a}} + \frac{l_{2}}{\sqrt{2 a l_{1}}} + \sqrt{\frac{2 l_{1}}{a}}] \times 2$

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A trough has two identical inclined segments and a horizontal segment. A ball is released on the top of one inclined part and it oscillates inside the trough. Friction is large enough to prevent slipping of the ball. Time period of oscillation is T. Now the liner dimension of each part of the trough is enlarged four times. Find the new time period of oscillation of the ball.