Question

Find the tension $T_1$ in the string. Assume all surfaces to be smooth.

• A. $3N$
• B. $6N$
• C. $2N$
• D. $4N$

Answer 1

The correct option is B $6N$

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

The force $F$ applied on the system is $F=9\sqrt{2}N$
So, the effective force that will cause the motion of the system is the horizontal component of the applied force i.e. $F_H=Fcos{45}^{\circ }=9\sqrt{2}\times \frac{1}{\sqrt{2}}=9N$
Hence, from FBDs we have
$T_2=a$..........(i)
$T_1-T_2=a$............(ii)
From eq (i) & (ii) we have
$T_1=2a$............(iii)
Also, we have
$F_H-T_1=a⟹9-T_1=a$ .....(iv)
Thus, from eq (iii) & (iv) we have,
$9=3a⟹a=3m/s^2$
Hence, $T_1=2a=6N$

Alternate:

Net force acting in the horizontal direction $=F\cos {45}^{\circ }=9\sqrt{2}\times \frac{1}{\sqrt{2}}=9\text{N}$
$a=\frac{\text{Supporting Force}}{\text{Total mass}}=\frac{9}{3}=3{\text{m/s}}^2$


From the FBD of the block we have,
$9-T_1=1.a$
$9-T_1=1\left(3\right)\Rightarrow T_1=6\text{N}$