Question

Consider the situation as shown in the figure. The system is released from rest and the block of mass $1kg$ is found to have a speed $0.3m/s$ after it has descended through a distance of $1m$. The coefficient of kinetic friction between the block and the table is (All pulleys are massless and smooth and strings are inextensible and light acceleration due to gravity $=10m/s^2$.):

• A. $0.12$
• B. $0.5$
• C. $0.2$
• D. $0.15$

Answer 1

The correct option is A $0.12$

If speed of block of $1.0kg$ is $0.3\frac{m}{s}$ then speed of $4.0kg$ block at this instant would be $0.6\frac{m}{s}$.

and $4$ kg block has moved a distance of $2m$ as $1kg$ block is moves through $1m$ distance.

Applying work energy theorem,
$E_i-E_f=$ work done against friction
$\therefore 0-\left[\frac{1}{2}\times 1.0\times (0.3{)}^2+\frac{1}{2}\times 4.0\times (0.6{)}^2-1\times 10\times 1\right]=\mu \times 4\times 10\times \left(2\right)$
Solving this equation, we get,
$\mu =0.12$