Three identical uniform thin metal rods form the three sides of an equilateral triangle. If the moment of inertia of the system of these three rods about an axis passing through the centroid of the triangle and perpendicular to the plane of

Question

Three identical uniform thin metal rods form the three sides of an equilateral triangle. If the moment of inertia of the system of these three rods about an axis passing through the centroid of the triangle and perpendicular to the plane of the triangle is n times. The moment of inertia of one rod separately about an axis passing through the centre of the rod and perpendicular to its length, the value of n is

Quantrex Academy · Accepted Answer

Correct answer: B. 6

Let the length of the rod be l . The moment of inertia of one rod separately about an axis passing through the centre of the rod and perpendicular to its length, I = I _ Ac +m r^2 aligned & = 1 12 m l^2+m ( l 2 3 )^2 & = m l^2 12 + m l^2 12 = 2 m l^2 12 aligned Moment of inertia of the system of 3rods =3 2 m l^2 12 =6 m l^2 12 =6 l According to the question 6 m l^2 12 =l=n ( m l^2 12 )n=6

Options

Correct answer

Step-by-step solution

More from Rotational Motion