A body of mass 5 kg undergoes a change in speed from 30 to 40m/s. Its momentum would increase by

Options

A. 50kgm/s
B. 75 kgm/s
C. 150 kgm/s
D. 350 kgm/s

Answer

To find the increase in momentum of a body with a mass of 5 kg that changes its speed from 30 m/s to 40 m/s, we can follow these steps:

### Step 1: Understand the formula for momentum
Momentum (P) is defined as the product of mass (m) and velocity (v):
\[ P = m \times v \]

### Step 2: Calculate the initial momentum (P1)
Given:
- Mass (m) = 5 kg
- Initial speed (V1) = 30 m/s

Using the formula for momentum:
\[ P1 = m \times V1 \]
\[ P1 = 5 \, \text{kg} \times 30 \, \text{m/s} \]
\[ P1 = 150 \, \text{kg m/s} \]

### Step 3: Calculate the final momentum (P2)
Given:
- Final speed (V2) = 40 m/s

Using the formula for momentum:
\[ P2 = m \times V2 \]
\[ P2 = 5 \, \text{kg} \times 40 \, \text{m/s} \]
\[ P2 = 200 \, \text{kg m/s} \]

### Step 4: Calculate the increase in momentum
The increase in momentum is given by the difference between the final momentum and the initial momentum:
\[ \text{Increase in momentum} = P2 - P1 \]
\[ \text{Increase in momentum} = 200 \, \text{kg m/s} - 150 \, \text{kg m/s} \]
\[ \text{Increase in momentum} = 50 \, \text{kg m/s} \]

### Final Answer:
The momentum would increase by **50 kg m/s**.

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