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A body of mass $1 k g$ is attached to an inextensible string of length $1 m$ , is made to rotate in vertical circle about the free end. When body is at its highest position, the tension in the string is $10 N$ . Then

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the tension in the string remains same for any position of the body

its velocity at highest position is $\sqrt{20} m / s$

its velocity at its lowest position is $\sqrt{50} m / s$

tension in the string at the lowest position of the body is $70 N$

answer is B, D.

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Detailed Solution

At the highest position, we have

$T_{1} + m g = \frac{m v_{1}^{2}}{r} \Rightarrow 10 + 1 \times 10 = \frac{1 v_{1}^{2}}{1} \Rightarrow v_{1} = \sqrt{20} \frac{m}{s}$

At the lowest position

$v_{2}^{2} = v_{1}^{2} + 2 g h = 20 + 2 \times 10 \times 2 = 60 \Rightarrow T_{2} = m g + \frac{m v_{2}^{2}}{r} = 1 \times 10 + \frac{1 \times 60}{1} = 70 N$

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