The mass of an object P is double the mass of Q. If both move with the same velocity, then the ratio of K.E. of P to Q is

Options

A. `1: 2 `
B. `2: 1`
C. `1: 4 `
D. `4: 1 `

Answer

To solve the problem, we need to find the ratio of the kinetic energy (K.E.) of two objects, P and Q, given that the mass of object P is double that of object Q, and both are moving with the same velocity.

### Step-by-Step Solution:

1. **Define the Masses**:
- Let the mass of object Q be \( m \).
- Therefore, the mass of object P will be \( 2m \) (since it is double the mass of Q).

2. **Define the Velocity**:
- Let the velocity of both objects P and Q be \( v \).

3. **Write the Formula for Kinetic Energy**:
- The formula for kinetic energy (K.E.) is given by:
\[ \text{K.E.} = \frac{1}{2} mv^2 \]

4. **Calculate Kinetic Energy of Object P**:
- Using the formula, the kinetic energy of object P (K.E.P) is:
\[ \text{K.E.P} = \frac{1}{2} \times (2m) \times v^2 = mv^2 \]

5. **Calculate Kinetic Energy of Object Q**:
- Similarly, the kinetic energy of object Q (K.E.Q) is:
\[ \text{K.E.Q} = \frac{1}{2} \times m \times v^2 = \frac{1}{2} mv^2 \]

6. **Find the Ratio of Kinetic Energies**:
- Now, we need to find the ratio of the kinetic energy of P to that of Q:
\[ \text{Ratio} = \frac{\text{K.E.P}}{\text{K.E.Q}} = \frac{mv^2}{\frac{1}{2} mv^2} \]
- Simplifying this gives:
\[ \text{Ratio} = \frac{mv^2}{\frac{1}{2} mv^2} = \frac{1}{\frac{1}{2}} = 2 \]

7. **Express the Ratio in Standard Form**:
- Therefore, the ratio of the kinetic energy of P to Q is:
\[ \text{Ratio} = 2:1 \]

### Final Answer:
The ratio of the kinetic energy of object P to object Q is \( 2:1 \).

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