Figure 103 SolutionThe mass starts from rest at A The string

Solution

The mass starts from rest at A. The string is in unstretched condition when it starts off from A.

Hence, the total energy at A will be only in the form of potential energy.

Now, it will gain some speed when it reaches B, plus the string will get stretched by d.

Equating the the total energies at A and B, we get:

2mgR = 0.5*m*v^2 + 0.5*k*d^2

Plus, the body is also in circular motion, hence the total centripetal force will be equal to m*v^2/R

Hence, K*d - mg = m^v^2 / R

Substituting the value for v^2 in equation 1 we get:

4mgR = KdR - mgR + kd^2

d = [-kR + sqrt(k^2R^2 + 20KmgR)] / 2k