Question

A block of mass $3\text{kg}$ is kept on a $6\text{kg}$ block and is kept on a smooth surface. The coefficient of static friction between them is $0.3$. A force $F$ is applied on the upper $3\text{kg}$ block and it is on the verge of slipping when the system moves together for a distance of $1\text{m}$. Calculate the work done by static friction on $3\text{kg}$ and $6\text{kg}$ respectively. (Take $g=10{\text{m/s}}^2)$

• A. $-9\text{J};9\text{J}$
• B. $0\text{J};0\text{J}$
• C. $18\text{J};-18\text{J}$
• D. None

Answer 1

The correct option is A $-9\text{J};9\text{J}$

By the FBD of both the blocks,


As $3\text{kg}$ is on the verge of slipping, frictional force is given by, $f_s={\mu }_s{N}_1=0.3\times 3\times 10$
$f_s=9N$

Since this $f_s$ acts opposite to motion
$\therefore$ work done by $f_s$ on $3\text{kg}$ body $=-f_s\times d$
$W_{3kg}=-9\text{J}$

For work done by $f_s$ on $6\text{kg}=9\text{J}$.
(Since $f_s$ is in direction of displacement we get positive work)

Hence option A is the correct answer