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A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

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a

mlω2k+mω

b

mlω2k−ωm

c

mlω2k+mω2

d

mlω2k−mω2

answer is D.

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Detailed Solution

Let say increase in the length of the spring = x and L =l+x be the total length of the spring during motion. The centripetal force acting on the particle is provided by the spring.∴mω2L = kx⇒mω2l+x=kx ⇒ lx+1=kmω2 ⇒ x=mlω2k−mω2

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A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is: