Question

The solid homogeneous cylinder is released from rest on the ramp. Determine the magnitude of the acceleration of the mass center.

a) gsin(θ)
b) gcos(θ)
c) gtan(θ)
d) g

Answer 1

The magnitude of acceleration of the mass center of a solid homogeneous cylinder released from rest on a frictionless ramp is a = g sin(θ), where g is the acceleration due to gravity and θ is the angle of the ramp.

Step-by-step explanation:

The acceleration of a mass center of a homogeneous cylinder released from rest on a ramp can be calculated using the principles of physics. When a cylinder rolls down a frictionless incline, the acceleration of the cylinder is given by a = g sin(θ), where g is the acceleration due to gravity and θ is the angle of inclination of the ramp.

This formula is derived from Newton's second law and the fact that the only force acting on the body along the slope is the component of its weight parallel to the slope, which is mg sin(θ). Since the acceleration does not depend upon the mass of the cylinder, all objects, irrespective of their mass, will accelerate at the same rate on a frictionless incline.