Question

Two blocks $m_{1}and{m}_2$ are placed on a smooth inclined plane as shown in figure. If they are released from rest. Find the tension in the string.

• A. $\sqrt{3}g$
• B. 1g
• C. $\frac{\sqrt{3}}{2}g$
• D. Zero

Answer 1

The correct option is C $\frac{\sqrt{3}}{2}g$

Gravitational Force on $m_2$ along the inclined plane in downward direction is,

$F_{G2}=m_{2}gsin{60}^0=1\times g\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}g}{2}$

Similarly, Gravitational Force on $m_1$ along the inclined plane in downward direction is,

$F_{G1}=m_{1}gsin{30}^0=\sqrt{3}\times g\times \frac{\sqrt{1}}{2}=\frac{\sqrt{3}g}{2}$

So net external force on the tow-block system is $F_{G2}-F_{G1}=0$

So acceleration of the blocks is also zero.

So Tension in the string balances the gravitational force on blocks along the inclined plane.

So tension, $T=F_{G2}=F_{G1}=\frac{\sqrt{3}g}{2}$