A simple pendulum of bob of mass `m` and length `L` has one of its ends fixed at the centre `O` of a vertical circle, as shown in the figure. If `0=60^(@)` at the point `P`, the minimum speed `u` that should be given to the bob so that it completes vetical circle is

Options

A. `sqrt(gL)`
B. `sqrt(2gL)`
C. `sqrt(5gL)/(2)`
D. `sqrt(3gL)/(2)`

Answer

B

Explanation

Energy conservation at heighest point
`{v_("top")=sqrt(gR)}`
`(1)/(2)m u^(2)=(mgR)/(2)+(1)/(2)m(sqrt(gR))^(2)rArru=sqrt(2gR)`