The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be

Question

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be (A) 0° (B) 30° (C) 45° (D) 60°

Tardigrade Admin · Accepted Answer

Free body diagram of m is

T = mg .....(i) Free body diagram of mass√2 m is

2T: cos θ=√2mg ...(ii) Dividing Eq. (ii) by Eq. (i), we get cosθ=(1/√2) or θ =45°

Q. The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $θ$ should be

$0^{\circ}$

$3 0^{\circ}$

$4 5^{\circ}$

$6 0^{\circ}$

Free body diagram of $m$ is

$T = m g .....$ (i)
Free body diagram of mass $2$ m is

$2 T cos θ = 2 m g ... (ii)$
Dividing Eq. (ii) by Eq. (i), we get
$cos θ = \frac{1}{2}$ or $θ = 4 5^{\circ}$

Q. The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be

0∘

30∘

45∘

60∘