1. Tardigrade
  2. Question
  3. Physics
  4. A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination 30° 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

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Q. A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination $30^{\circ}$ 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

Laws of Motion

Solution:

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

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