A particle of mass M rests on a straight groove along which it is constrained to move. A perfectly elastic rubber band of natural length l and uniform area of cross-section is attached with the particle. The other end of the band is suspended from a rigid support. A force K(l '2 - l 2 ) 1/2 is required to stretch the band to a length l'. The particle is moved to a distance S (where S << 1) and then released. Taking K =
and μ μ as the coefficient of friction between the particle and the groove, the velocity of particle when passing through the initial position is

Text Solution
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Let the particle be at a distance x at any instant and T be the tension in the string then
T = K (l' 2 – l 2 ) 1/2 = Kx
Net force tending to make the particle move further through dx.
Work done = 

= 
or v = 
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