Explanation:
Given that,
(1). Mass of solid cylinder A= 100 g
Radius = 10 cm
Mass of solid cylinder B= 200 g
Radius = 10 cm
(2). Mass of solid cylinder A= 100 g
Radius = 10 cm
Mass of solid cylinder B= 100 g
Radius = 20 cm
We need to calculate the moment of inertia of solid cylinder A and B
Using formula of moment of inertia
But we know that,
For pure rolling rotation,
An object under the influence of gravity does not depend on the object's mass and its size.
Therefore, Both solid cylinders reach on same time.
(3). Mass of solid cylinder A= 100 g
Radius = 10 cm
Mass of hollow cylinder B= 100 g
Radius = 10 cm
We need to calculate the moment of inertia of solid cylinder A
Using formula of moment of inertia
We need to calculate the moment of inertia of hollow cylinder B
Using formula of moment of inertia
Here, The moment of inertia of A is less for hollow cylinder.
Therefore, Solid cylinder will reach first.
(4). Mass of solid cylinder A= 100 g
Radius = 10 cm
Mass of solid sphere B= 100 g
Radius = 10 cm
We need to calculate the moment of inertia of solid cylinder A
Using formula of moment of inertia
We need to calculate the moment of inertia of solid sphere B
Using formula of moment of inertia
Here, The moment of inertia of A is more for solid sphere.
Therefore, Solid sphere will reach first
Hence, This is the required solution.