The moment of inertia of a uniform solid regular tetrahedron of mass m and edge a, about its symmetry axis (i.e and axis passing through on evertex and the centre of the opposite face) is:

Options

A. `ma^(2)//10`
B. `3ma^(2)//10`
C. `ma^(2)//15`
D. `ma^(2)//20`

Answer

D

Explanation

For an equilateral triangle of side a, moment of inertia is `(ma^(1))/(12)`about an axis passing through its CM and perpendicular to plane - the result of the integration is similar to that of a solid cone along its axis: a factor of `3//5`
`1 = (3)/(5) ((ma^(2))/(12))`