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Q.

The Young's modulus of a rope of 10m length and having diameter of 2 cm is 20 x 1011  dyne cm-2. If the elongation produced in the rope is 1 cm, the force applied on the rope is

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a

6.28 x 105 N 

b

6.28  x 104 N

c

6.28 x 104 dyne 

d

 6.28 x 105 dyne

answer is B.

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Detailed Solution

Young's modulus of a rope,  Y=FLAΔl

Given,  L=10m,A=πr2=π(1)2=π

Y=20×1011 dyne cm−2,Δl=1cm

⇒ F=Y⋅A⋅ΔlL⇒F=20×1011×π×110×102

F=6.28×109 dyne 

 or  F=6.28×104N

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