Q.

A 0.1kg mass is suspended from a wire of negligible mass. The length of the wire is 1m  and its cross sectional area is 4.9×107 m2 . If the mass is pulled  slightly in the vertically downward direction and then released, it performs simple harmonic motion of angular frequency  140 rad/s. Then the Young’s modulus of material of the wire is(Assume that the Hooke’s law is valid throughout the motion )

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a

5×108 N/m2

b

4×109 N/m2

c

4×108 N/m2

d

14×109 N/m2

answer is A.

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Detailed Solution

We know that  ω=km……….. (i)
Here  Y=FLAlF=YALl
Comparing the above equation with F=kl we get 
k=YAL…….. (ii)
From equations (i) and (ii) we get 
140=Y×4.9×1070.1×1
Y=4×109 N/m2 
Therefore, the correct answer is (A).
 

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