A body of mass m hangs at one end of a string of length l, the other and of which is fixed . It is given a horizontal velocity so that the string would just reach where it makes an angle of `30^@` with the vertical . The tension in the string at mean position is

Options

A. `mg(5-2sqrt(3))`
B. `mg(3-3sqrt(3))`
C. `mg(3-sqrt(3))`
D. `mg(4-sqrt(3))`

Answer

C

Explanation

When body is released from the position P (inclined at angle `theta`fromvertical) then velocity at mean position
`v=sqrt(2gl(1-costheta))`
`therefore " ""Tension at the lowest poits"=mg+(mv^2)/(l)`
`=mg+(m)/(l)" "[2gl(cos30)]`
`=mg+(m)/(l)" "[2gl(2-sqrt(3)/(2))] `
`mg+2mg(2-sqrt(2))=mg(5-2sqrt(3))`