Question

A rope of mass $2m$ is used to pull a block of mass $m$ as shown in the figure. Find the force exerted by the rope on the block. Assume all surfaces as frictionless.

• A. $\frac{F}{2}$
• B. $\frac{2F}{3}$
• C. $\frac{F}{3}$
• D. $\frac{F}{4}$

Answer 1

The correct option is C $\frac{F}{3}$

Consider the block and the rope as a system initially.
Acceleration of the system $=a=\frac{F}{m+2m}=\frac{F}{3m}$ (i)
Let $T$ be the tension in the rope due to force $F$.
Let us draw FBD of both rope and the block:


Using FBD of block, we can say
$T=m\times a$ (ii)
Using equation (i) in (ii), we get
$T=m\times \frac{F}{3m}=\frac{F}{3}$
Hence, force exerted by the rope on the block, $T=\frac{F}{3}$