Question

In the arrangement shown in the figure, the coefficient of friction between the two blocks is $\mu =0.5$ and the surface is smooth. The force of friction acting between the two blocks is

• A. $10\text{N}$
• B. $12\text{N}$
• C. $8\text{N}$
• D. $4\text{N}$

Answer 1

The correct option is C $8\text{N}$

The FBDs of the blocks are as shown


From the FBD we have
$N_1=2g=20\text{N}$
Maximum friction between the two blocks is
$f_{\text{max}}=\mu N_1=0.5\times 20=10\text{N}$

Let us assume that the blocks move together towards left with the common acceleration. Then,
$a=\frac{f-2}{2}=\frac{20-f}{4}$
$\Rightarrow 2f-4=20-f\Rightarrow f=8\text{N}$
Since, $8\text{N}<10\text{N}$ i.e. $f<f_{\text{max}}$, our assumption is right.

Hence, friction between the two blocks is $f=8\text{N}$