Question

Find the value of $F$, if the tension in the string $T_1=36\text{N}.(g=10{\text{m/s}}^2$)

• A. $50\text{N}$
• B. $60\text{N}$
• C. $80\text{N}$
• D. $160\text{N}$

Answer 1

The correct option is C $80\text{N}$

FBDs of all the masses are as shown
Let the system's acceleration is towards the applied force


So, from FBD of mass $3Kg$ we have
$T_1-3g=3a⟹a=\frac{T_1-3g}{3}=\frac{36-30}{3}=2m/s^2$
Also, from FBD of $2Kg$ mass
$T-T_1-2g=2a⟹T=2\times 2+36+20=60N$
And, from the FBD of $10Kg$ mass
$F-T=10a⟹F=10\times 2+60=80N$

Alternate:

Acceleration of the system is given by,
$a=\frac{\text{Supporting Force - Opposing Force}}{\text{Total mass}}$
$=\frac{F-5g}{15}\dots \dots \left(1\right)$
So, from FBD of $3Kg$ mass we have,
$T_1-3g=3a⟹T_1=3(g+a)\Rightarrow 36=3(g+a)$
$\Rightarrow a=2{\text{m/s}}^2$
From (1)
$2=\frac{F-5g}{15}\Rightarrow F=80\text{N}$