A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions as shown in the figures below. In which case, if any, is the magnitude of the tension along the string largest?

a.A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions image 1

b.A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions image 2

c.A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions image 3

d.A block of weight W is suspended by a string of fixed length. The ends of the string are held at various positions image 4

Answer: a

Solution:

From the free body diagrams

2Tcosθ = W

Hence, T = W/2cosθ.

If the θ increases then cosθ will decrease and θ increase as tension increases. Thus the tension will be maximum when θ is maximum.

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