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

Options

A. `3.75`
B. `4.25`
C. `2.75`
D. `4.00`

Answer

A

Explanation

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 `