Question

A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M easily slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time from the top of their inclined planes,

A) the cylinder will reach the bottom first.
B) the block will reach the bottom first.
C) the block will reach the bottom with the greater kinetic energy.
D) the cylinder will reach the bottom with the greater kinetic energy.
E) both the block and the cylinder will reach the bottom at the same time.

Answer 1

The block will reach the bottom first and with greater kinetic energy because it does not have any rotational kinetic energy to convert its gravitational potential energy to.

Step-by-step explanation:

The block will reach the bottom first, and it will also have the greater kinetic energy. When the block slides down the inclined plane, all of its gravitational potential energy is converted into kinetic energy. However, when the hollow cylinder rolls down the inclined plane, some of its gravitational potential energy is converted into both linear and rotational kinetic energy.

Since the block does not have any rotational kinetic energy, all of its gravitational potential energy is converted into linear kinetic energy, resulting in a greater speed compared to the cylinder. Therefore, the block reaches the bottom first and with greater kinetic energy.

Answer 2

Step-by-step explanation:

block will go down with acceleration = g sinθ

cylinder will go down with acceleration

= g sinθ / (1 + k² / r²)

this value is less than g sinθ

so block will have greater acceleration so it will reach bottom earlier.

A ) is correct.

the block will reach the bottom with the greater kinetic energy.

C ) is correct

Both the body loses same potential energy but cylinder will have both rotational and linear kinetic energy . Hence cylinder will have less kinetic energy because their linear velocity is less. It is due to distribution of potential energy into rotational and linear kinetic energy.