Question

A marble is placed at the bottom of a semi-spherical bowl, as shown in the figure. The marble is then displaced from the bottom of the bowl to a position about halfway from the top of the bowl. The marble is then released from rest such that the marble always remains in contact with the bowl. Students observe that the marble rolls back and forth as it oscillates about the bottom of the bowl. Which of the following statements best explains why the marble undergoes oscillatory motion?

a)The sides of the bowl become steeper at positions farther from the bottom of the bowl.b) The net force exerted on the marble always has a component directed toward the bottom of the bowl. c) The normal force exerted on the marble decreases with increasing distance from the bottom of the bowl. D ) The gravitational force exerted on the marble is constant in magnitude and direction.​

Answer 1

The marble oscillates in the bowl due to the net force directed toward the bowl's bottom, creating a restoring force that ensures simple harmonic motion until dissipative forces bring it to rest.

Step-by-step explanation:

The marble undergoes oscillatory motion when released from a position about halfway from the top of a semi-spherical bowl because the net force exerted on the marble always has a component directed toward the bottom of the bowl (option b). This force is known as the restoring force which is directed towards the stable equilibrium point at the bottom of the bowl. As the marble rolls up the side of the bowl, gravity acts to slow it down until it stops and rolls back towards the center, creating oscillatory motion or simple harmonic motion (SHM). This oscillatory motion continues, with the marble rising to increasingly lower heights on either side of the bowl due to dissipative forces such as friction, which gradually decrease the amplitude of the oscillation until the marble comes to rest at the equilibrium point at the bottom of the bowl.

Answer 2

It is D

Step-by-step explanation: