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

Options

A. `sqrt(gl)`
B. `sqrt(2 gl)`
C. `sqrt((5 gl)/(2))`
D. `sqrt(1.5 gl)`

Answer

B

Explanation

`- mgl (1 - cos theta) = (1)/(2) mv^(2) - (1)/(2) m u^(2)` …(1)
Also to just complete circle, `T = 0` at highest point. So,
`mg = (mv^(2))/(l)`
`v = sqrt(gl)` ….(2)
from (1) & (2) and using `theta = 60^(@)`
get `u sqrt(2 gl)`