Laws of Motion - Result Question 62
62. A body of mass $0.4 kg$ is whirled in a vertical circle making $2 rev / sec$. If the radius of the circle is $1.2 m$, then tension in the string when the body is at the top of the circle, is [1999]
(a) $41.56 N$
(b) $89.86 N$
(c) $109.86 N$
(d) $115.86 N$
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Answer:
Correct Answer: 62. (a)
Solution:
- (a) Given : Mass $(m)=0.4 kg$ Its frequency $(n)=2 rev / sec$
Radius $(r)=1.2 m$. We know that linear velocity of the body $(v)=\omega r=(2 \pi n) r$ $=2 \times 3.14 \times 2 \times 1.2=15.08 m / s$.
Therefore, tension in the string when the body is at the top of the circle (T)
$ \begin{aligned} & =\frac{mv^{2}}{r}-mg=\frac{0.4 \times(15.08)^{2}}{2}-(0.4 \times 9.8) \\ & =45.78-3.92=41.56 N \end{aligned} $
