Question

A small ball is suspended in a cart moving with uniform acceleration 'a' by two identical inextensible cords A and B. If tension in the cord A is twice that in cord B. Then 'a' will be :

• A. $\frac{g}{2}m/s^2$
• B. $\frac{g}{\sqrt{3}}m/s^2$
• C. $\frac{g}{3\sqrt{3}}m/s^2$
• D. $\frac{g}{2\sqrt{3}}m/s^2$

Answer 1

The correct option is C $\frac{g}{3\sqrt{3}}m/s^2$

First consider x component force, $2T\sin 30-T\sin 30=ma,Tsin30=ma,T=2ma$
For y-component force, $2Tcos30+Tcos30$

$=mg,3T\times \frac{\sqrt{3}}{2}=mg$
$=6ma\times \frac{\sqrt{3}}{2}=mg$
$a=\frac{g}{3\sqrt{3}}m/s^2$