Question

A bob of mass $m$ is suspended from the ceiling of a train moving with an acceleration $a$ as shown in figure. Find the angle $\theta$ in equilibrium position.

• A. $ta{n}^{-1}\frac{a}{g}$
• B. $ta{n}^{-1}\frac{g}{a}$
• C. $co{t}^{-1}\frac{a+g}{a-g}$
• D. None of these

Answer 1

The correct option is A $ta{n}^{-1}\frac{a}{g}$

From the frame of reference of train, there is pseudo force of $ma$ on bob in backward direction.

Balancing force in horizontal direction, $Tsin\theta =ma$

Balancing force in vertical direction, $Tcos\theta =mg$

Taking ratio, $\frac{sin\theta }{cos\theta }=\frac{a}{g}$

$⟹tan\theta =\frac{a}{g}⟹\theta =ta{n}^{-1}\frac{a}{g}$