Question

Find the tension in the string.

• A. $82.5\text{N}$
• B. $95.5\text{N}$
• C. $100.2\text{N}$
• D. $102\text{N}$

Answer 1

The correct option is A $82.5\text{N}$

Let the acceleration $a$ of the 5 kg block be towards right

So, from the FBDs of both the masses, we have
$15g-T=15a$.....................(i)
$T-60=5a$..........................(ii)
On solving both the equation (i) & (ii) we have,
$a=4.5m/s^2$
Thus, from the FBD of $15Kg$ body, tension $T$ in the string is given as
$15g-T=15a⟹T=15(g-a)=15\times 5.5$
$⟹T=82.5N$

Alternate:

Supporting force $15g=15\times 10=150\text{N}>60\text{N}$
Hence, $15\text{kg}$ body will move downwards. So, the acceleration of the system is given by
$a=\frac{\text{Supporting Force - Opposing force}}{\text{Total mass}}$
$=\frac{150-60}{20}=\frac{90}{20}=4.5{\text{m/s}}^2$

So, from FBD of $5\text{kg}$ body tension $T$ in the string is given as
$T-60=5a$
$\Rightarrow T=60+5\left(\frac{9}{2}\right)=82.5\text{N}$