A body of m kg slides from rest along the curve of a vertical circle from point A to B in a frictionless path. The velocity of the body at B is _

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Solution

Q.
A body of m kg slides from rest along the curve of a vertical circle from point A to B in a frictionless path. The velocity of the body at B is ______.

$(given, R = 14 m, g = 10 {m/s}^{2} and \sqrt{2} = 1.4)$ [2024]

1 21.9 m/s

2 10.6 m/s

3 19.8 m/s

4 16.7 m/s

Ans.
(1)

By conservation of mechanical energy, decrease in P.E. = increase in K.E.

$m g (R + \frac{R}{\sqrt{2}}) = \frac{1}{2} m v_{B}^{2} - 0 \Rightarrow 2 g R (1 + \frac{1}{\sqrt{2}}) = v_{B}^{2}$

$\Rightarrow v_{B}^{2} = 2 \times 10 \times 14 \times (1 + \frac{1}{1.4})$

$v_{B} = \sqrt{20 \times 24} = 4 \sqrt{30} \approx 21.9 m/s$

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