Laws of Motion · Question 21

A body of mass m is suspended by two strings making angles 1 and 2 with the horizontal ceiling with tensions T1 and T2 simultaneously. T1 and T2 are related by T1 = 3T2, the angles 1 and 2 are

1. 1 = 30 , 2 = 60 with T2 = 3mg4
2. 1 = 45 , 2 = 45 with T2 = 3mg4
3. 1 = 30 , 2 = 60 with T2 = 4mg5
4. 1 = 60 , 2 = 30 with T2 = mg2

Answer

(4) 1 = 60 , 2 = 30 with T2 = mg2

Solution

The body is in equilibrium under T1, T2 and mg.

Horizontal: T1 1 = T2 2 3 1 = 2

1 = 60 , 2 = 30 : 3 12 = 32 ✓ ( 1 = 30 , 2 = 60 gives 32 12; 45 , 45 gives 3 1)

Vertical: T1 1 + T2 2 = mg

3T2 32 + T2 12 = mg

2T2 = mg T2 = mg2

Answer: (4)