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Questions  

A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination 30o with horizontal. The acceleration of train up the plane is a = g/2. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is 

a
30∘
b
tan−1⁡(2/3)
c
tan−1⁡(3/2)
d
tan−1⁡(2)

detailed solution

Correct option is B

Tsin⁡θ−mgsin⁡30∘=ma⇒ Tsin⁡θ=mgsin⁡30∘+mg/2   .....(i) Tcos⁡θ=mgcos⁡30∘    .....(ii)Dividing Eqs. (i) by (ii), we gettan⁡θ=23

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