Question

A block of mass M is pulled along a horizontal rough surface by a rope of mass m by applying a force F at one end of the rope. f is the friction between block and the surface. The force which the rope exerts on the block is:

• A. $\frac{FM}{m+M}+f$
• B. $\frac{mF}{m+M}-f$
• C. $\frac{mf+FM}{M+m}$
• D. $\frac{MF-fm}{M-m}$

Answer 1

Answer: (C)

$\frac{mf+FM}{M+m}$

Friction force is only applied on $M$, it is $f$.
$(M+m)a=F-f\Rightarrow a=\frac{F-f}{M+m}$
So, the force due to rope is: $Ma+f=\frac{mf+FM}{M+m}$