Question

In the shown figure, assume pulley is massless and frictionless. Calculate the acceleration of the blocks if blocks are released from rest.

$\begin{align}
  & \text{A}\text{. }\dfrac{m}{M+m}g \\
 & \text{B}\text{. }\dfrac{M}{M+m}g \\
 & \text{C}\text{. }\dfrac{M}{m}g \\
 & \text{D}\text{. }\dfrac{M-m}{M+m}g \\
\end{align}$

Answer 1

Hint: At first we need to draw the diagram and show the free body diagram of the image given in the question. Then we need to find the equation according to the free body diagram. Then if we equate all the equations we will get the required result.

Complete answer:

In the above diagram we see that, on the left there is a system of pulley where the pulley is massless and frictionless. On the strings of the pulley we see tension ‘t’ is working. On the right side we see the free body diagram of the two bodies.
Now, let us consider the acceleration of the blocks to be ‘a’.
Now, we are considering the free body diagram of mass M that is the bigger block visually, we get,
$Ma=Mg-T$ ,………….Eq.1
Now, we are considering the free body diagram of mass ‘m’ that is the smaller mass visually, we get,
$ma=T-mg$,…………. Eq.2
Now on solving equation 1 and equation 2 we get,
$a=\dfrac{M-m}{M+m}g$ ,

So, the correct answer is “Option D”.

Additional Information:
A pulley is generally a wheel with grooves that is supported on a shaft or axle and it is designed in such a way that it can do movement or change direction.

Note:
While making the free body diagram we need to be careful to consider all the forces and that are affecting the body. We must note that the mass of the two bodies are different. Solve the equation carefully so that no errors are there.