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The Young's modulus of a rope of 10 m le...

The Young's modulus of a rope of 10 m length and having diameter of 2 cm is `20xx10^(11)` dyne `cm^(-2)` . If the elongation produced in the rope is 1 cm, the force applied on the rope is

A

`6.28xx10^(5) N`

B

`6.28 xx 10^(4)` N

C

`6.28 xx 10^(4)` dyne

D

`6.28 xx 10^(5)` dyne

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Young's modulus of a rope , `Y=(FL)/(A Delta l)`
Given, L=10 m , `A=pir^(2)=pi(1)^(2)=pi`
`Y=20xx10^(11)` dyne `cm^(-2), Deltal=1 cm`,
`F=(Y*A*Deltal)/(L)implies (20xx10^(11)xxpixx1)/(10xx10^(2))`
`F=6.28xx10^(9)` dyne
`F=6.28xx10^(4)` N
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