If the linear momentum is increased by 50%, then KE will be increased by :

Options

A. 0.5
B. 1
C. 12.5
D. 0.25

Explanation

To solve the problem of how kinetic energy (KE) changes when linear momentum (p) is increased by 50%, we can follow these steps:

### Step 1: Define Initial Momentum and Kinetic Energy
Let the initial linear momentum be \( p \). The formula for kinetic energy in terms of momentum is given by:

\[ KE = \frac{p^2}{2m} \]

where \( m \) is the mass of the object.

### Step 2: Calculate the Increased Momentum
If the linear momentum is increased by 50%, the new momentum \( p' \) can be expressed as:

\[ p' = p + 0.5p = 1.5p \]

### Step 3: Calculate the New Kinetic Energy
Now, we can calculate the new kinetic energy \( KE' \) using the new momentum:

\[ KE' = \frac{(p')^2}{2m} = \frac{(1.5p)^2}{2m} \]

Calculating \( (1.5p)^2 \):

\[ (1.5p)^2 = 2.25p^2 \]

Thus, the new kinetic energy becomes:

\[ KE' = \frac{2.25p^2}{2m} \]

### Step 4: Relate New Kinetic Energy to Initial Kinetic Energy
We already know from Step 1 that the initial kinetic energy \( KE \) is:

\[ KE = \frac{p^2}{2m} \]

Now, we can express the new kinetic energy \( KE' \) in terms of the initial kinetic energy:

\[ KE' = 2.25 \cdot \frac{p^2}{2m} = 2.25 \cdot KE \]

### Step 5: Calculate the Increase in Kinetic Energy
The increase in kinetic energy can be calculated as:

\[ \Delta KE = KE' - KE = 2.25 \cdot KE - KE = (2.25 - 1) \cdot KE = 1.25 \cdot KE \]

### Conclusion
The increase in kinetic energy is \( 1.25 \) times the initial kinetic energy.