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Question

# A 1 kg stone at the end of a 1 m long string is whirled in a vertical circle at a constant speed of 4 m/s. The tension in the string is 6 N when the stone is (Take g=10 m/s2)

A
At the top of the circle.
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B
At the bottom of the circle.
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C
Half way down
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D
None of above
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Solution

## The correct option is A At the top of the circle. Suppose the string is making an angle θ with the verical On balancing the forces along the length of the string, T=mgcosθ+mv2R ----- (1) where, R=1 m,v=4 m/s ,m=1 kg (given) Tension T=6 N Putting all these values in equation (1), we get: 6=1×10×cosθ+1×421 ⇒6=10cosθ+16 ⇒cosθ=−1 ⇒θ=180∘ {With the vertical} So, the stone will be at the top of the circle.

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