Question

The moment of inertia of a rod about an axis through its centre and perpendicular to it is 1/12ML²
(where M is the mass and L is te length of the rod).
The rod is bent in the middle so that the two halves make an angle of 60°. the moment of inertia of the
bent rod about the same axis would be
(A)1/48ML²
(B)1/12ML²
(C)1/24ML²
(D)ML²/8(3)½​

Answer 1

answer : option (B) 1/12 ML²

explanation : a/c to question, a rod of mass m is bent in the middle so that the two halves make an angle 60° with each other as shown in figure.

so, mass of each part M/2 and length of each part of rod is L/2 .

dear, here a interesting thing is that we have to find moment of inertia about same axis. as it is clearly shown that, if the centre of rod was O, then we have to find M.I about O .

we know, moment of inertia about its one end , I = 1/3 ml²

here m = M/2 and l = L/2

so, I1 = 1/3 (M/2)(L/2)² = 1/24 ML²

similarly, moment of inertia of second part of rod about its one end , I2 = 1/24 ML²

so, moment of inertia of system = I1 + I2

= 1/24 ML² + 1/24 ML²

=1/12 ML²

hence, option (B) is correct choice.

Answer 2

Answer:

Explanation:

Option :