If the mass of a moving body decreased by one third of its initial mass and velocity is tripled, then the percentage change in its kinetic energy is

Options

A. `500%`
B. `600%`
C. `300%`
D. `200%`

Explanation

To solve the problem step by step, we will calculate the initial and final kinetic energies, find the change in kinetic energy, and then determine the percentage change.

### Step 1: Calculate Initial Kinetic Energy (K1)
The formula for kinetic energy (K) is given by:
\[ K = \frac{1}{2} mv^2 \]
Let the initial mass be \( m \) and the initial velocity be \( v \). Therefore, the initial kinetic energy \( K_1 \) is:
\[ K_1 = \frac{1}{2} mv^2 \]

### Step 2: Determine Final Mass (m2)
The mass of the body decreases by one third of its initial mass. Thus, the final mass \( m_2 \) can be calculated as:
\[ m_2 = m - \frac{1}{3}m = \frac{2}{3}m \]

### Step 3: Determine Final Velocity (v2)
The velocity is tripled, so the final velocity \( v_2 \) is:
\[ v_2 = 3v \]

### Step 4: Calculate Final Kinetic Energy (K2)
Now we can calculate the final kinetic energy \( K_2 \) using the final mass and final velocity:
\[ K_2 = \frac{1}{2} m_2 v_2^2 \]
Substituting the values of \( m_2 \) and \( v_2 \):
\[ K_2 = \frac{1}{2} \left(\frac{2}{3}m\right) (3v)^2 \]
\[ K_2 = \frac{1}{2} \left(\frac{2}{3}m\right) (9v^2) = \frac{2}{3}m \cdot \frac{9}{2}v^2 = 3mv^2 \]

### Step 5: Relate K2 to K1
We know from Step 1 that:
\[ K_1 = \frac{1}{2} mv^2 \]
Thus, we can express \( K_2 \) in terms of \( K_1 \):
\[ K_2 = 3mv^2 = 6 \left(\frac{1}{2} mv^2\right) = 6K_1 \]

### Step 6: Calculate Change in Kinetic Energy (ΔK)
The change in kinetic energy \( \Delta K \) is given by:
\[ \Delta K = K_2 - K_1 = 6K_1 - K_1 = 5K_1 \]

### Step 7: Calculate Percentage Change in Kinetic Energy
The percentage change in kinetic energy is given by:
\[ \text{Percentage Change} = \left(\frac{\Delta K}{K_1}\right) \times 100\% \]
Substituting the values we found:
\[ \text{Percentage Change} = \left(\frac{5K_1}{K_1}\right) \times 100\% = 5 \times 100\% = 500\% \]

### Final Answer
The percentage change in kinetic energy is **500%**.

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