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A pendulum has a ball of mass m attached...

A pendulum has a ball of mass m attached to the stringa and is suspended from the roof of a trolley. If the trolley rolls upwards with acceleration a, then what is the angle made by the string with the inclined plane? (Given that, `a=5m//s^(2), g=10m//s^(2)` and the angle of inclination of the plane is `30^(@)`)

A

`cos^(-1)((2)/(sqrt3))`

B

`cot^(-1)((2)/(sqrt3))`

C

`sin^(-1)((2)/(sqrt3))`

D

`tan^(-1)((2)/(sqrt3))`

Text Solution

Verified by Experts

The correct Answer is:
B
In equilibrium,
`T cos theta=ma+mg sin alph`
`T sin theta =mg cos alpha`

This gives, `cot theta=(a+g sin alpha)/(g cos alpha)`
`=(5+10xx((1)/(2)))/(10xx(sqrt3)/(2))=(2)/(sqrt3)`
`therefore" "theta=cot^(-1)((2)/(sqrt3))`
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