Question

A steel ball is suspended from the accelerating frame by the two chords $A$ and $B$. Determine the acceleration $a$ of the frame which will cause the tension in $A$ to be twice that of $B$?

• A. $a=\frac{g}{\sqrt{27}}$
• B. $a=\frac{g}{3}$
• C. $a=\frac{g}{\sqrt{3}}$
• D. $a=\frac{2g}{\sqrt{27}}$

Answer 1

The correct option is A $a=\frac{g}{\sqrt{27}}$

As the frame is accelerating, a pseudo force will act on it in opposite direction.

on balancing the forces on the mass,

$2T\cos 30+T\cos 30=mg\to \left(1\right)$

$2T\cos 60=maT\cos 60$

$T\cos 60=ma$

$T=2ma\to \left(2\right)$

Putting the value of $T$ in equation $\left(1\right)$, we get,

$\frac{3\sqrt{3}\times 2ma}{2}=mg$

$a=\frac{g}{\sqrt{27}}$