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Each of three blocks shows in figure has...

Each of three blocks shows in figure has a mass 3 kg. The wire connecting blocks A and B has area of cross-section `0.005 cm^(2)` and Young's modulus of elasticity ` Y = 2 xx 10 ^(11) N//m^(2)` . Neglect friction. Find the elasticity potential energy stored per unit volume in wire connecting blocks A and B in steady state.
`(Taken g = 10 m//s^(2))`

A

` 500 J//m^(3)`

B

`1000 J//m^(3)`

C

`2000 J//m^(3)`

D

`3000 J//m^(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
(b)
From force diagram ,
T=3a `" "…(i)`
`T_(1)-T=3a" "…(ii)`
`3g-T_(1)=3a " "…(iii)`
After solving Eqs. (i) and (ii) , we get T=10N
`therefore` Stress `=(T)/(A)=(10)/(0.005xx10^(-4))`

`therefore` The elastic energy stored per unit volume `=(1)/(2)xx"stress" xx "strain" =(1)/(2) xx "stress"xx("stress")/(Y)(because Y=("stress")/("mass"))=("stress"^(2))/(2Y)=((10)/(0.005xx10^(-4)))^(2)/(2xx2xx10^(11))`
`(100)/(25xx10^(-6)xx10^(-8)xx4xx10^(11))=(100)/(100x10^(-14)xx10^(11))`
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