A mass `m` of radius `r` is rolling horizontally without any slip with a linear speed `v`. It then rolls up to a height given by `(3)/(4)(v^(2))/(g)`

Options

A. the body is identified to be a disc or a solid cylinder
B. the body is a solid sphere
C. moment of inertia of the body about instantaneous axis of rotation is `(3)/(2)mr^(2)`
D. moment of inertial of the body about instantaneous axis of rotation is `(7)/(5)mr^(2)`

Explanation

To solve the problem of a mass \( m \) rolling without slipping and reaching a height of \( \frac{3}{4} \frac{v^2}{g} \), we can follow these steps:

### Step 1: Understand the Energy Conservation Principle
When the mass rolls up to a height, its kinetic energy is converted into potential energy. The total mechanical energy is conserved since there is no external work done (assuming no friction losses).

### Step 2: Write the Initial Kinetic Energy
The total kinetic energy \( KE \) of a rolling object consists of translational and rotational kinetic energy:
\[
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