Question

In the figure shown, the coefficient of friction between all surfaces in contact is $0.4$. Taking $g=10m/s^2$, find the tension $T$ in the string.

• A. $10N$
• B. $12N$
• C. $14N$
• D. $20N$

Answer 1

The correct option is C $14N$

Let us consider $2kg$ and $3kg$ as the system as they are having same coefficient of friction and in contact with the surface.
So, the FBDs of the system can be drawn as shown

From the FBD we have the acceleration of the system as
$a=\frac{\text{(Supporting force-opposing force)}}{\text{Total mass}}$
opposing force=Friction force $\left(f\right)=\mu \left(2g\right)+\mu \left(3g\right)=5\mu g$
$\Rightarrow a=\frac{5g-f}{10}=\frac{5g-\left(\mu 5g\right)}{10}$
$\Rightarrow a=\frac{5g(1-\mu )}{10}=\frac{5g(1-0.4)}{10}=3m/s^2$

Now, we have FBD of $2kg$ mass

So, from FBD we have,
$T-f=ma\Rightarrow T=f+ma$
$\Rightarrow T=\mu N+ma=0.4\left(2g\right)+2a$
$\Rightarrow T=0.4\times 20+2\times 3=14N$