Question

A block B of mass m placed on a horizontal frictionless surface is tied to a point A on a vertical wall by mean of a massless string going over a frictionless moveable pulley P as shown in the figure. A force F is applied to the pulley as shown. The acceleration of the block is

• A. $\frac{2F}{m}$
• B. $\frac{F}{m}$
• C. $\frac{F}{2m}$
• D. Zero

Answer 1

The correct option is C $\frac{F}{2m}$

Figure (b) shows the free body diagram of the pulley.
The forces acting on the pulley are:
(i) F towards right
(ii) tension T towards left by portion PA of the string
(iii) tension T towards left by portion PB of the string
Since the mass of the pulley is zero, we have
$F-T-T=0$
$\Rightarrow T=\frac{F}{2}$
Now, for the block, the only horizontal force is tension T acting towards right, its acceleration is
$a=\frac{T}{m}=\frac{F}{2m}$