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A simple pendulum is vibrating with an a...

A simple pendulum is vibrating with an angular amplitude of `90^(@)` as shown in figure. For what value of `alpha` (angle between string and vertical) during its motion, the total acceleration is directed horizontally ?

A

`90^(@),cos^(-1)((1)/(sqrt3))0^(@)`

B

`0^(@),cos^(-1)sqrt3,90^(@)`

C

`0^(@),cos^(-1)sqrt3,90^(@)`

D

`cos^(-1)((1)/(sqrt3))90^(@),0^(@)`

Text Solution

Verified by Experts

What a is horizontal

`tanalpha=(a_(n))/(a_(t))=(v^(2)//l)/(g sinalpha)=(2gh//l)/(g sinalpha)`
`=(2glcosalpha//l)/(gsinalpha)=2cot alpha`
`rArr" "tanalpha=sqrt2`
or `cosalpha=(1)/(sqrt3)`
`therefore" "alpha=cos^(-1)((1)/(sqrt3))`
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