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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 4.9×10−7 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

4×109 N/m2

b

14×109 N/m2

c

4×108 N/m2

d

5×108 N/m2

answer is A.

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Detailed Solution

We know that ω=km……….. (i)Here Y=FLAl⇒F=YALlComparing the above equation with F=kl we get k=YAL…….. (ii)From equations (i) and (ii) we get ∴ 140=Y×4.9×10−70.1×1∴Y=4×109 N/m2 Therefore, the correct answer is (A).

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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 4.9×10−7 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 )