Question

In the given system, the pulley is light and frictionless; string is also massless. Initially the system is in equilibrium. Now a small block $C$ of mass $m$ is placed on the block $B$ of mass $M$ . If block $C$ always remains on block $B$ , find the normal reaction on $C$ due to $B$ .

Accepted Answer

As both the blocks $C$ have same mass, initially both will be in equilibrium. When the block $M$ is placed on the block $C$ , the system will start accelerating with some acceleration.

For calculation of that acceleration, we can consider $B and C$ as same object and consider its mass as $(M + m)$ .

Now, consider FBD of ( $M + m$ ),

As it is moving downwards, we can write,

$(M + m) g - T = (M + m) a \dots (1)$

Now consider FBD of mass $A$ ,

As this block is moving in upward direction, we can write,

$T - M g = M a \dots (2)$

Solving equation $(1)$ and $(2)$ , we will get,

$a = \frac{[(M + m) - M]}{[(M + m) + M]} g = \frac{mg}{(2 M + m)}$

The block $B + C$ Combined will move down with acceleration $a$ .

Now analysing the block $C$ With respect to block $B$ .

As block $B$ Is moving in downward direction with acceleration, hence it is non-inertial frame of reference, this why pseudo force is applied on block $C$ .

Hence, from FBD of $C$ , we can write, $N = m g - m a$ (from reference of $B, C$ will appear to be at rest).

Substituting value of $a$ in the above equation, we can write,

$\Rightarrow N = m g - m (\frac{m g}{2 M + m}) = \frac{2 M m g}{(2 M + m)}$

In the given system, the pulley is light and frictionless; string is also massless. Initially the system is in equilibrium. Now a small block $C$ of mass $m$ is placed on the block $B$ of mass $M$ . If block $C$ always remains on block $B$ , find the normal reaction on $C$ due to $B$ .

Important Questions on Newton's Laws of Motion (Without Friction)

Learn and Prepare for any exam you want !

In the given system, the pulley is light and frictionless; string is also massless. Initially the system is in equilibrium. Now a small block C of mass m is placed on the block B of mass M. If block C always remains on block B, find the normal reaction on C due to B.

Important Questions on Newton's Laws of Motion (Without Friction)

Learn and Prepare for any exam you want !

In the given system, the pulley is light and frictionless; string is also massless. Initially the system is in equilibrium. Now a small block $C$ of mass $m$ is placed on the block $B$ of mass $M$ . If block $C$ always remains on block $B$ , find the normal reaction on $C$ due to $B$ .