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. ${\tan }^{-1}$ (a/g)
• B. ${\cos }^{-1}$ (a/g)
• C. ${\cot }^{-1}$ (a/g)
• D. ${\sin }^{-1}$ (a/g)

Answer 1

The correct option is A

${\tan }^{-1}$ (a/g)

Non-inertial frame of reference (Train)
FBD of bob w.r.t train. (real forces + pseudo force):

With respect to train, bob is in equilibrium
$\sum F_x=0\Rightarrow Tsin\theta =ma$ ..........(i)
$\sum F_y=0\Rightarrow Tcos\theta =mg$ .........(ii)
From Eqs (i) and (ii), we get the result
$\theta =ta{n}^{-1}$ (a/g)