A varible force `P` is amintained targent to a frictionless cylinder surface of radius a as shown in the figure. By slowly varying this force, a block of weight `W` is moved and the spring to which it is streched from position `1` to position `2`. The work done by the force `P` is:

Options

A. `W a sin theta`
B. `(1)/(2) ka^(2) theta^(2)`
C. `W a sin theta + ka^(2) theta^(2)`
D. `W a sin theta + (1)/(2) ka^(2) theta^(2)`

Answer

B

Explanation

Increase in height of block . `h = a sin theta`
Increase in length of spring `x = a theta`
Work done by `P = mgh + P = mgh + (1)/(2) kx^(2)`
`Wa sin theta + (1)/(2) ka^(2) theta^(2)`