A simple pendulum of length l has a maximum angular displacement `theta`. The maximum kinetic energy of the bob of mass m will be

Options

A. `(1)/(2)(ML)/(g)`
B. `(Mg)/(2L)`
C. `MgL (1-"cos" alpha)`
D. `(MgL "sin" alpha)/(2)`

Answer

C

Explanation

For maximum angular displacement it is a B and its K.E. =0 and its `P.E.=Mgh =Mg[L-L "cos" alpha]`
`=MgL [1-"cos" alpha]`
Total energy at `B=MgL[1-"cos" alpha]`

At the lowest position A, its P.E.=0 and K.E. will be maximum `(K_(m))`
`therefore` Total energy at `A=0 + K_("max")`
From the principle of conservation of energy,
`MgL[1-"cos" alpha]=K_("max")`