A pendulum bob has a speed of `3ms^(-1)` at its lowest position. The pendulum is `0.5` m long. The speed of the bob, when string makes an angle of `60^(@)` to the vertical is `("take, g"=10ms^(-1))`

Options

A. `2ms^(-1)`
B. `(1)/(2)ms^(-1)`
C. `1 ms^(-1)`
D. `2.5ms^(-1)`

Answer

A

Explanation

`h=R(1-cos60^(@))=(R)/(2)`

`because` In right angled `DeltaAOB`,
`cos60^(@)=(OA)/(AB)rArr(1)/(2)=(0.5-h)/(R)rArrR=1-2h`
`rArr" "2h=1-2h" "(becauseR=2h)`
`rArr" "4g=1rArrh=(1)/(4)`
`because" "v=sqrt(u^(2)-2gh)=sqrt(9-2xx10xx(1)/(2))=sqrt(9-5)=2ms^(-1)`
`therefore" "v=2ms^(-1)`