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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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