Question

In the figure shown below, two blocks of same mass are at rest and a horizontal force $F$ is applied on $5kg$ block towards left. If the coefficient of friction between the surfaces are $0.5$ and $0.5$ as shown in the figure, find the value of tension in the rope and force required just to slide the bottom block. Take $g=10m/s^2$.

• A. $T=15\text{N},F=50\text{N}$
• B. $T=25\text{N},F=50\text{N}$
• C. $T=15\text{N},F=75\text{N}$
• D. $T=25\text{N},F=75\text{N}$

Answer 1

The correct option is D $T=25\text{N},F=75\text{N}$

The FBDs of the blocks are as shown.
As per the question, condition is limiting since the block will just slide.


From the FBD, we have at equilibrium
$N_1=5g=50\text{N}$
$f_1=T$

At limiting condition,
$f_1=\mu N_1=0.5\times 50=25\text{N}$
$\therefore T=25\text{N}$

Also, we have
$N_2=N_1+5g=50+50=100\text{N}$
and $F=f_1+f_2$
$f_2={\mu }_2{N}_2=0.5\times 100=50\text{N}$ at limiting condition
$\Rightarrow F=25+50=75\text{N}$