Question

Two blocks $A$ and $B$ of masses $m_A=1kg$ and $m_B=2kg$ are placed in contact on a frictionless plane of inclination ${30}^{\circ }$. Find the magnitude of contact force between the two blocks when an external force is applied on the blocks as shown in the figure.

• A. $2N$
• B. $6N$
• C. $12N$
• D. $10N$

Answer 1

The correct option is D $10N$

We can consider both the blocks as a system of $3kg$ as they move same acceleration.
F.B.D of the system will be

From FBD, we can write
$F\cos {30}^{\circ }-mg\sin {30}^{\circ }=ma$
$20\sqrt{3}\times \frac{\sqrt{3}}{2}-30\times \frac{1}{2}=3a$
$⟹a=5m/s^2$ (i)
Let $N^{\prime }$ be the contact force between the two blocks.
Now, FBD of $1kg$ block will be

From FBD, we can say
$N^{\prime }-g\sin {30}^{\circ }=1\times a$ (ii)
Using equation (i) in (ii), we get
$N^{\prime }-5=5$
$⟹N^{\prime }=10N$