Question

A thin and uniform rod of mass m and length is held vertically on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact point with the floor without slipping. Which of the following statements is/are correct?

(a) The angular acceleration is zero.
(b) The linear acceleration of the center of mass is g.
(c) The rod will rotate about its center of mass.
(d) Both (b) and (c).

Answer 1

The correct statement is (d) Both (b) and (c). When the rod is released, the angular acceleration is zero, the linear acceleration of the center of mass is g, and the rod will rotate about its center of mass.

Step-by-step explanation:

The correct statement is (d) Both (b) and (c).

When the thin and uniform rod is released from rest and falls by rotating about its contact point with the floor without slipping, the angular acceleration is indeed zero (statement a). This is because there is no torque acting on the rod about its center of mass, so the angular momentum is conserved.

The linear acceleration of the center of mass is g (statement b). This is because gravity provides an unbalanced force that accelerates the rod's center of mass downward.

The rod will rotate about its center of mass (statement c). This is because the contact point with the floor provides a normal force that acts through the center of mass, creating a torque and causing the rod to rotate about its center of mass.