The moment of inertia about x-axis of uniform thin plate of density `rho kg//m^(2)` as shown in the figure is `(Nrho a^7)/(21)`, then find the value of N.

Options

A. 1
B. 2
C. 4
D. 6

Answer

B

Explanation

`dl = 1/2 dx xx (2y)^(2)`
`dl = 1/12 (2y)^(3) dx rho`
`l = 1/12 xx 8 rho xx int_(0)^(4) x^(6)dx`
`implies I = 2/3 xx (a^(2)rho)/(7) = (2a^(2)rho)/(2l) , N =2`.