Question

A man of mass $50\text{kg}$ is pulling a rope on a plank of mass $100\text{kg}$ kept on a smooth surface as shown, with force of $100\text{N}$. If both man and plank move together, find force of friction acting on man.
Given coefficient of friction between man and plank is $\frac{1}{6}$.

• A. $\frac{100}{3}\text{N towards left}$
• B. $\frac{100}{3}\text{N towards right}$
• C. $\frac{250}{3}\text{N towards left}$
• D. $\frac{250}{3}\text{N towards right}$

Answer 1

The correct option is A $\frac{100}{3}\text{N towards left}$

For man
$T-f=50a$
For plank
$T+f=100a$
$\Rightarrow 2T=150a\Rightarrow a=\frac{2\times 100}{150}=\frac{4}{3}{\text{ms}}^{-2}$
$\because T-f=50a\therefore 100-f=50\frac{4}{3}$
$\Rightarrow f=\frac{100}{3}\text{N towards left}$