If momentum is increased by 20%, then kinetic energy increases by

Options

A. 0.48
B. 0.44
C. 0.4
D. 36%.

Explanation

To solve the problem, we need to determine how much the kinetic energy increases when the momentum is increased by 20%. We will follow these steps:

### Step 1: Understand the relationship between momentum and kinetic energy
The kinetic energy (KE) is related to momentum (p) by the formula:
\[ KE = \frac{p^2}{2m} \]
where \(m\) is the mass of the object.

### Step 2: Define the initial momentum
Let the initial momentum be \(p\).

### Step 3: Calculate the new momentum after a 20% increase
If the momentum is increased by 20%, the new momentum \(p'\) can be calculated as:
\[ p' = p + 0.2p = 1.2p \]

### Step 4: Calculate the initial kinetic energy
Using the initial momentum, the initial kinetic energy \(KE_1\) is:
\[ KE_1 = \frac{p^2}{2m} \]

### Step 5: Calculate the new kinetic energy with the increased momentum
Now, we calculate the new kinetic energy \(KE_2\) using the new momentum \(p'\):
\[ KE_2 = \frac{(p')^2}{2m} = \frac{(1.2p)^2}{2m} = \frac{1.44p^2}{2m} \]

### Step 6: Find the percentage increase in kinetic energy
To find the percentage increase in kinetic energy, we use the formula:
\[ \text{Percentage Increase} = \frac{KE_2 - KE_1}{KE_1} \times 100\% \]
Substituting the values we found:
\[ \text{Percentage Increase} = \frac{\frac{1.44p^2}{2m} - \frac{p^2}{2m}}{\frac{p^2}{2m}} \times 100\% \]
This simplifies to:
\[ = \frac{1.44p^2 - p^2}{p^2} \times 100\% = \frac{0.44p^2}{p^2} \times 100\% = 0.44 \times 100\% = 44\% \]

### Conclusion
Thus, when the momentum is increased by 20%, the kinetic energy increases by **44%**.

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