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A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30^\circ$ and $60^\circ$ from the vertical (lowest position) are $T_1$ and $T_2$ respectively. Then

1. $T_1=T_2$
2. $T_2>T_1$
3. $T_1>T_2$
4. Tension in the string always remains the same

Correct answer: $T_1>T_2$

Solution

In a vertical circle, tension depends on both speed and the radial component of weight. At $30^\circ$ from the lowest position, the particle is lower than at $60^\circ$, so the required tension is greater there. Hence $T_1>T_2$.

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