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Q.

When a particle of mass m is suspended from a massless spring of natural lengthℓ , the length of the spring becomes 2ℓ . When the same mass moves in conical pendulum as shown in figure, the length of the spring becomes L. The radius of the circle of conical pendulum is:

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a

LL−ℓL(L−ℓ)

b

LL−ℓL(L−2ℓ)

c

L(L−ℓ)

d

L2−2ℓ2

answer is B.

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Detailed Solution

mg=kℓ (1)k(L−ℓ)1−R2L2=kℓ (2)1−R2L2=ℓ2(L−ℓ)2{(L−ℓ)2−ℓ2(L−ℓ)2}L2=R2R=(LL−ℓ) (L2−2Lℓ)

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When a particle of mass m is suspended from a massless spring of natural lengthℓ , the length of the spring becomes 2ℓ . When the same mass moves in conical pendulum as shown in figure, the length of the spring becomes L. The radius of the circle of conical pendulum is: