Question

Figure shows a quarter circle. A particle moves
from B to O with 5 m/s, from O to A with 7 m/s.
With what speed the particle should move from
A to B so that average speed for total journey is
6 m/s?

Options :-
$\begin{gathered} \tt{ a) \: \: \frac{210}{35 - \frac{4}{\pi} } \: \: ms ^{ - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: b) \: \: \frac{210}{31 - \frac{4}{\pi} } \: \: ms ^{ - 1} }\\ \\ \tt{c) \: \: \frac{210}{35 - \frac{\pi}{4} } \: \: ms ^{ - 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: d) \frac{205}{35 - \frac{\pi}{4} } \: \: ms ^{ - 1} }\end{gathered} \ \textless \ br /\ \textgreater$
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Answer 1

Explanation:

This requires that the particle must have some minimum speed. At the top (point A): Let v1 be the speed of the particle and T1 the tension in the string. Here, both T → 1 and weight is vertically downward. Hence, the net force on the particle towards the centre O is T1 + mg, which is the necessary centripetal force.