Which among the following is an expression for energy?

Options

A. `V^2It`
B. `V^2Rt`
C. `V^2t/R`
D. `V^2t^2/R`

Answer

D

Explanation

If M is mass of the square plate before cutting the holes, the mass of portion of each hole
`m=(M)/(16R^(2))xxpiR^(2)=(Mpi)/(16)`
`therefore` Moment of inertia of remaining portion about Z-axis
`I=I_(("square"))-4xxI_(("hole"))`
`=(M)/(12)(16R^(2)+16R^(2))-4[(mR^(2))/(2)+m(sqrt(2)R)^(2)]`
`=(M)/(12)(32R^(2))-(10MR^(2))`
`=(8)/(3)MR^(2)-(10)/(16)MR^(2)pi`
`therefore I=((8)/(3)-(10pi)/(16))MR^(2)`