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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-a9e0ovkc6x60ujqz.jpg" /> (A) 45 °  (B) 60 °  (C) 0 °  (D) 30 °

Tardigrade Admin · Accepted Answer

The tension in both the strings will be same.
Solution

For equilibrium in vertical direction for body

B

we have

2 m g = 2 T cos θ

∴ 2 m g = 2 (m g) cos θ

(

∵ T = m g

at equilibrium)

∴ cos θ = \frac{1}{2} \Rightarrow 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

$4 5^{\circ}$

$6 0^{\circ}$

$0^{\circ}$

$3 0^{\circ}$

The tension in both the strings will be same.

For equilibrium in vertical direction for body $B$ we have
$2 m g = 2 T cos θ$
$∴ 2 m g = 2 (m g) cos θ$
( $∵ T = m g$ at equilibrium)
$∴ cos θ = \frac{1}{2} \Rightarrow θ = 4 5^{\circ}$

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

45∘

60∘

0∘

30∘