Inside of a train a ball of weight W is hanging by a light wire at rest from the ceiling. The wire makes an angle θ with the ceiling, as shown in the figure. Which one of the following conditions must be true about the tension T in the wire?
A) T sin θ = W
B) T cos θ = W
C) T tan θ = W
D) T = W
E) T = ma

Question

Inside of a train a ball of weight W is hanging by a light wire at rest from the ceiling. The wire makes an angle θ with the ceiling, as shown in the figure. Which one of the following conditions must be true about the tension T in the wire? 
A) T sin θ = W 
B) T cos θ = W 
C) T tan θ = W 
D) T = W 
E) T = ma

Quizplus · Accepted Answer

The ball is at rest and therefore, the forces acting on the ball are balanced. The only two forces acting on the ball are its weight, W, acting downwards and the tension, T, acting upwards. These two forces are perpendicular to each other and therefore, we can resolve them into horizontal and vertical components. Let the angle between the tension and the ceiling be $	heta$.

The vertical component of tension is T sin $	heta$ which acts upwards and balances the weight W acting downwards. Therefore, T sin $	heta$ = W is the condition that must be true.

Inside of a Train a Ball of Weight W Is