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One end of a wire 2 m long and damete...

One end of a wire 2 m long and dameter 2 mm is fixed in a celling . A naughty boy of mass 10 kg jumps to catch the free end and stays, there. The chamge is length of wire is `(Take r = 10 m//s^(2), Y= 2 xx 10^(11) N//m^(2)`)

A

`3.1 85 xx 10^(-5)`

B

2 mm

C

3 mm

D

4mm

Text Solution

Verified by Experts

The correct Answer is:
A
(a) For equilibrium of the boy,
Tension in wire, T=weight of boy= mg = 100N
`=(100xx10^(6))/(3.14) N//m^(2)implies "strain"=(DeltaL)/(L)=(DeltaL)/(2)`
`therefore Y=("stress")/("strain")=(100xx10^(6)xx2)/(3.14 xx Delta2`
`therefore DeltaL=(100xx10^(6)xx2)/(3.14xx2xx10^(11))=31.85xx10^(-5) m`
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