Question

Block $A$ weighs $4kg$ and block $B$ weighs $8kg$. Coefficient of kinetic friction between all surfaces in contact is $0.2$. The force $F$ necessary to drag the block $B$ at constant speed if $A$ is held at rest as shown in the figure is
(Take $g=10m/s^2$)

• A. $12\text{N}$
• B. $16\text{N}$
• C. $24\text{N}$
• D. $32\text{N}$

Answer 1

The correct option is D $32\text{N}$

The FBDs of the blocks are as shown.
As per the question, the acceleration of block $A$ and $B$ will be zero.


From the FBD, we have
For $4kg$ block :
$N_1=4g=40\text{N}$
$f_1=\mu N_1=0.2\times 40=8\text{N}$

For $8kg$ block :
$N_2=N_1+8g=40+80=120\text{N}$
$f_2=\mu N_2=0.2\times 120=24\text{N}$

Now, from the FBD of block of mass $8kg$ we get
$F-f_1-f_2=ma=0$
(because block moves with constant velocity)
$\Rightarrow F=f_1+f_2=8+24=32\text{N}$