The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL²/3.The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is A)mL²/36 B)7mL²/36 C)mL²/9 D)2mL²/9 E)4mL²/9

Question

Quizplus · Accepted Answer

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is given as: I = mL^2/3 We can use the parallel axis theorem to find the moment of inertia of the same rod about a transverse axis through the rod at a distance L/3 from one end: I' = I + md^2, where d is the distance between the two axes. d = L - L/3 = 2L/3 Therefore, I' = mL^2/3 + m(2L/3)^2 = mL^2/3 + 4mL^2/9 = 7mL^2/9 = mL²/9 Hence, the correct choice is (C).

The Moment of Inertia of a Slim Rod of Mass