CGPET 2015 Solved Paper

Work done is stretching a wire by Δx
ΔW = ΔV = potential energy stored in the wire
=

1

2

×stress×strain×volume
=

1

2

×Y×strain×strain×volume
=

1

2

×Y×(strain)2×(AL)
=

1

2

×Y×(

ΔL

L

)2×(A1L1)
where, symbols have their usual meanings.
For first wire,
ΔW1=

1

2

×Y(

ΔL1

L1

)2×(A1L1)
For second wire,
ΔW2=

1

2

×(

ΔL2

L2

)2×(A2L2)
Thus, we can write,

ΔW2

ΔW1

=(

ΔL2

ΔL1

)2×(

L1

L2

)2×(

A2L2

A1L1

)
=(

1‌mm

1‌mm

)2×(

L

L∕2

)2×(

L∕2

2

)×(

2r

r

)2
=1×4×

1

2

×4=8
⇒ΔW2=8(ΔW1)=8(2J)=16J