A cylinder and a solid disc are released from rest from the top of a ramp.They roll down the hill without slipping. Which statement iscorrect?

a. The cylinder reaches the bottom first
b. The disc reaches the bottom first
c. They both reach the bottom at the same time
d. Could be any of the above depending on the relative sizes and masses of the disc and the cylinder.

I say D,am I right?

Do a computation. Write down the formula for the total kinetic energy of a rolling object. Leave the moment on intertia undetermined. Express the angular velocity in terms of the velocity (assume that the object has a radius of R).

If you write the result as:

E_kin = A/2 m v^2

then what is A?

Yes, you are correct. The correct statement is option D: "Could be any of the above depending on the relative sizes and masses of the disc and the cylinder." The time it takes for the cylinder and the disc to reach the bottom of the ramp will depend on their respective sizes and masses.

Yes, you are correct. The correct answer is (d) Could be any of the above depending on the relative sizes and masses of the disc and the cylinder.

To understand why this is the correct answer, we need to consider the factors that affect the time it takes for the objects to reach the bottom of the ramp.

When a cylinder or a solid disc rolls down a ramp without slipping, the motion is determined by both translational motion (the object's center of mass moving downward) and rotational motion (the object rotating as it moves downward). The speed at which an object rolls depends on the combination of these two motions.

The time it takes for an object to roll down the ramp depends on its moment of inertia (which depends on the shape and mass distribution), its mass, and how these factors affect the torque and therefore the acceleration of the object.

In the case of a cylinder and a solid disc, the key factor that determines their relative speeds down the ramp is their moment of inertia. The moment of inertia of a cylinder is given by (1/2) * m * r^2, where m is the mass of the cylinder and r is its radius. The moment of inertia of a solid disc is given by (1/2) * m * r^2, where m is the mass of the disc and r is its radius.

If the cylinder and the disc have the same mass and radius, then their moments of inertia are also the same. In this case, both objects will experience the same torque and acceleration as they roll down the ramp. Therefore, they will reach the bottom at the same time (option c).

However, if the cylinder and the disc have different masses and/or radii, their moments of inertia will be different. In this case, their torques and accelerations will also be different. As a result, one object may reach the bottom before the other, depending on their relative sizes and masses. Therefore, the answer could be any of the above options (a, b, or c) depending on the specific properties of the cylinder and the disc.