Young's modulus experiment is performed on a steel wire of 1 m length and 8 mm diameter. The mass required to be added in the experiment to produce 5 mm elongation of the wire is `(Y_(steel) = 2 xx 10^9 Nm^(-2) . g=10m//s^2)`

Options

A. 25 kg
B. 50 kg
C. 250 kg
D. 500 kg

Answer

B

Explanation

Given , L = 1m, ` r = d/2 = 4 mm = 4 xx 10^(-3) m`
` Delta l = 5mm = 5 xx 10^(-3) m`
` Y = (mgL)/(pi r&2 Delta l) rArr m = (Y pi r^2 Delta l)/(gL)`
` = (2 xx 10^9 xx 3.14 xx (4 xx 10^(-3) )^2 xx (5 xx 10^(-3) ) )/(10 xx 1)`
` = (2 xx 3.14 xx 16 xx 5 )/(10 ) = 50.24 kg ~~ 50 kg `