The angular momentum of a rigid body of mass m about an axis is n times the linear momentum (P) of the body. Total kinetic energy of the rigid body is

Options

A. `(n^(2) p^(2))/(2)`
B. `(P^(2)[ 1 + n^(2)] )/(2m)`
C. `(n^(2) P^(2))/(2m)`
D. `n^(2) P^(2) xx 2`m

Answer

A, C

Explanation

Angular momentum,
L = `I omega`, given, L = nP
Total kinetic energy
`= (P^(2))/(2m) + (L^(2))/(2I) = (P^(2))/(2m) + (n^(2) P^(2))/(2I)`
= `(P^(2))/(2) ((1)/(m) + (n^(2))/(I))`
It is impossible to calculate the total kinetic energy as no information in given about the moment of inertia `I` of the rigid body.
Besides, P = r`beta` and given L = n`beta`. Therefore , the dimension of n is equal to the dimension of r. So, the dimension of the kinetic energy does not match with any one of the dimensions of the four options.
the equestion is incorrect or incomplete.