First slide

Inertial and uniformly accelerated frame of reference

Question

A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination 30^owith 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

Difficult

A

$30^{\circ}$
B

$\tan^{- 1} (2 / \sqrt{3})$
C

$\tan^{- 1} (\sqrt{3} / 2)$
D

$\tan^{- 1} (2)$

Solution

$\begin{array}{l} T \sin θ - m g \sin 30^{\circ} = m a \\ \Rightarrow T \sin θ = m g \sin 30^{\circ} + m g / 2 . . . . . (i) \\ T \cos θ = m g \cos 30^{\circ} . . . . . (i i) \end{array}$
Dividing Eqs. (i) by (ii), we get
$\tan θ = \frac{2}{\sqrt{3}}$

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