1 . 
A particle of mass " m " rests on a straight groove along which it is constrained to move . The mass is attached to a vertical rubber band suspended froma rigid support . Initially , the band is of its natural length " L " . The rubber band has the property the in order to stretch it to a length " L0 " , a force " K ( L 2 - L02 ) 1 / 2 " must be applied .
The mass " m " is pulled aside along the groove by a small amount " D , D <<< L " and then released . If " μ " is the co - efficient of friction between the groove and the mass , calculate the velocity of the mass when it passes through its initial position , assuming the rubber band to be perfectly elastic .Take " K = m gD " .
21thant's easy i think ( may be i m wrong)
work done by friction=
Wf =(theta 0) ∫0u(mg - F0cos (theta)) dx
where F0 = force given by rubber band( can be written in terms of theta)
its easy to find the P.E of rubber band when its elongated by an amount x
Now we have x = L tan (theta) (where x is the distance from the mean point)
Differentiate dx = L sec2(theta)d(theta)
Now chnge in KE = work done by all forces
