Question

Problem 12c

Answer 1

Given information

There are one sphere and one cylinder both have the same mass and the same radius.

Step-by-step explanation

Step 1.

Consider both the sphere and cylinder roll down an plane that is inclined at an angle with ground without slipping.

At the top of the plane the object has only potential energy, which is

 

Here, is the total energy at the top, is the mass of the object, is the acceleration due to gravity and is the height.

At the bottom of the plane, the object has transnational kinetic energy and rotational kinetic energy.

The total energy of the object at the bottom is

      

Here, is the total energy and  is the kinetic energy.

According to the law of conservation of energy, the total energy of the system remains conserved. Therefore, the energy at the top of the plane is equal to the energy at the bottom.

Equate two formulae of energies and solve to calculate the kinetic energy of the object.