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Question

# A mass of 2 kg is whirled in a horizontal circle at an initial speed of 5 r.p.m. Keeping the radius constant the tension in the string is doubled. The new speed is nearly.

A
7r.p.m.
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B
14r.p.m.
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C
10r.p.m.
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D
20r.p.m.
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Solution

## The correct option is D 7r.p.m.Given : m=2kgInitial speed of rotation f1=5 r.p.mLet the radius of the circle be r∴ Tension in the string T1=mrw21 where w1=2πf1⟹ T2=4π2mrf21 ....................(1)Now the tension in the string is doubled i.e T2=2T1 ∴ T2=4π2mrf22OR 2T1=4π2mrf22 ..........(2)Dividing (2) by (1), 2=f2252 ⟹f2≈7 r.p.m

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