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A pendulum is hanging from the ceiling o...

A pendulum is hanging from the ceiling of a car having an acceleration `a_(0)` with respect to the road. Find the angle made by the string with vertical at equilibrium. Also find the tension in the sting in this position

Text Solution

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A) `T sin theta = ma_(0)`…….(i)
`T cos theta = mg`……..(ii)
`therefore tan theta =a_(0)/g, therefore` the string is making an angle

`tan^(-1)(a_(0)/g)` with vertical at equilibrium
B) squaring and adding (i) and (ii)
`T^(2) sin theta + T^(2) cos theta =m^(2) (a_(0)^(2) + g^(2))`
`T=msqrt(a_(0)^(2) +g^(2))`
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