Question

Two blocks $A$ and $B$ of equal mass are connected by a light inextensible taut string passing over two light smooth pulleys fixed to the blocks. The parts of the string not in contact with the pulleys are horizontal. A horizontal force $F$ is applied to the block $A$ as shown. There is no friction, then

• A. the acceleration of $A$ will be equal to that of $B$
• B. the acceleration of $A$ will be less than that of $B$
• C. the sum of rate of changes of momentum of $A$ and $B$ is greater than the magnitude of $F$
• D. the sum of rate of changes of momentum of $A$ and $B$ is equal to the magnitude of $F$

Answer 1

The correct option is A the acceleration of $A$ will be equal to that of $B$

Draw free body diagram,

$⟹$ Rate of change of momentum gives us force acting on the particle.

So, net force on the system is, $F$.

$⟹$ Acceleration of $A=\frac{F-2T}{m}$

acceleration of $A=\frac{3T}{m}$

So, we cant comment on its acceleration.