A metal wire of negligible mass, length 1 m and cross-sectional area `10^(-6) m^(2)` is kept on a smooth horizontal table with one end fixed on the table. A ball of mass 2kg is attached to the other end of the wire. When the wire and the ball are rotated with angular velocity of 20 rad/s, it is found that the wire is elongated by `10^(-3)m`. If the Young's modulus of the metal is `n xx 10^(11) N//m^(2)`, then the value of n is

Options

A. 6
B. 8
C. 9
D. 10

Answer

B

Explanation

When the wire and the ball are rotated, the centrifugal force `mRomega^(2)` acts on the ball and as a result the wire clongates.
`because Y = (FL)/(ADeltaL) but F = mRomega^(2)`
`:. Y = (mRomega^(2)L)/(ADeltaL) = (mR^(2)omega^(2))/(ADeltaL) " " (because L = R)`
`= (2 xx 1^(2) xx 20 xx 20)/(10^(-6) xx 10^(-3))`
` Y = 8 xx 10^(11) N//m^(2)`
But it is given that, `Y = n xx 10^(11) N//m^(2) " " n = 8`