Question

An L-shaped body is constructed out of two identical thin rods of length L and mass M. The point of joining is P, and the two rods are perpendicular to each other. The distance of the center of mass of this body from P is:

(a) L/2
(b) L/√2
(c) L/3
(d) L/4

Answer 1

The distance of the center of mass of the L-shaped body from the point of joining is L/3.

Step-by-step explanation:

In this problem, the two rods are identical and perpendicular to each other, forming an L shape. To find the distance of the center of mass of this body from the point of joining (P), we can use the concept of moment of inertia. The moment of inertia of a rod about its center of mass is given by ML^2/12, where M is the mass of the rod and L is the length of the rod.

Since the rods are identical and perpendicular, the center of mass of each rod will be at a distance of L/2 from the point of joining. Using the parallel-axis theorem, the moment of inertia of the whole body about the point of joining is the sum of the individual moments of inertia of the two rods. Therefore, the total moment of inertia of the body is (ML^2/12) + (ML^2/12).

To find the distance of the center of mass from the point of joining, we need to find the total mass of the body. Since both rods have the same mass (M), the total mass of the body is 2M. Using the equation for center of mass, we have: distance of center of mass = (moment of inertia about the point of joining) / (total mass).

So, the distance of the center of mass of this L-shaped body from the point of joining is (ML^2/6) / (2M), which simplifies to L/3.