Question

Two blocks A and B of masses $m_A=1kg$ and $m_B=2kg$ are placed in contact on a frictionless incline 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. $10N$
• B. $6N$
• C. $2N$
• D. None of these

Answer 1

The correct option is B $6N$


We can consider both the blocks as a system of mass $3kg$ as they move with same acceleration.

FBD of the system will be




$F-Mg\sin \theta =Ma$
$\Rightarrow 18-30\sin {30}^{\circ }=3a$
$\Rightarrow a=1m/s^2$

Let $N^{\prime }$ be the the contact force between the two blocks.



Drawing F.B.D of $1kg$ block separately,



$N^{\prime }-m_{A}g\sin \theta =m_{A}a$
$\Rightarrow N^{\prime }-10\sin {30}^{\circ }=1$
$\Rightarrow N^{\prime }=6N$