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A brass rod of cross-sectional 1 cm^(2) ...

A brass rod of cross-sectional `1 cm^(2)` and length 0.2 m is compresssed lengthwire by a weight of 5kg. The young's modulus of elasticity of brass is `1 xx 10^(11) N//m^(2)` and `g = 10m//sec^(2)`. What is the increases in the energy of the rod ?

A

`10^(-5) J`

B

`2.5 xx 10^(-4) J`

C

`2.5 xx 10^(-5) J`

D

`5 xx 10^(-5) J`

Text Solution

Verified by Experts

The correct Answer is:
C
Given : `F = 5 xx 10 = 50 N, A = 1 cm^(2) = 10^(-4) m^(2)`
Energy stored per unit volume `= (1)/(2) xx (("stress")^(2))/(Y)`
`:.` Energy stored `= (1)/(2) xx (("stress")^(2))/(Y) xx "volume of the wire"`
`= (1)/(2) xx ((F)/(A))^(2) xx (Al)/(Y)`
`= (1)/(2) . (F^(2)L)/(AY)`
`= (1)/(2) xx (50 xx 50 xx 0.2)/(10^(-4) xx 10^(11))`
`= (250)/(10^(7)) = 2.5 xx 10^(-5) J`
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