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A load of 10 KN is supported from a pul...

A load of `10 KN` is supported from a pulley , which in turn is supported by a rope of cross-sectional area `10^(3) mm^(2)` and modulus of elasticity `10^(3) Nmm^(-2)` as shown in the figure. Neglecting friction at the pulley , then downward deflection of the load (in mm) is

A

`3.75`

B

`4.25`

C

`2.75`

D

`4.00`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `T` be the tension in the rope . Then,
2T =10 kN
` rArr T=5000 N `
Longitudinal stress in the rope is
`sigma =(T)/(A) =(5000 N)/(10^(3)mm ^(2)) = 5 N mm^(-2)`
Extension in the rope `= (stress)/(Y)xxL`
` 5/10^(3)xx(600+900) = 7.5 mm`
:. Downward deflection of the load `= 7.5/2 = 3.75 mm `
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