Question

Find the tension $T_1$ in the string. All surfaces are smooth.

• A. $30N$
• B. $40N$
• C. $50N$
• D. $60N$

Answer 1

The correct option is C $50N$

The FBDs of the masses are as shown
Let the direction of the acceleration be as shown in the figure

So, from the FBDs we have,
$T_2=3a$............(i)
And, $T_1-T_2=2a$.................(ii)
From eq (i) & (ii) we have
$T_1=5a$.............(iii)
Also, $100-T_1=5a$............(iv)
$\therefore$ from eq (iii) & (iv) we have
$100=10a⟹a=10m/s^2$
Thus, $T_1=5a⟹T_1=5\times 10=50N$

Alternate:

Acceleration of the system is given by,
$a=\frac{\text{Supporting Force}}{\text{Total mass}}=\frac{100}{10}=10{\text{m/s}}^2$


From the FBD of $5Kg$, we have
$100-T_1=5a$
$T_1=100-5\left(10\right)=50\text{N}$