A force acting on an object of mass 500 g changes its speed from 200 cm/s to 0.2 m/s. The change in momentum is

Options

A. increase by 0.90 N s
B. decrease by 0.90 N s
C. increase by 90 g cm/s
D. decrease by 90 g cm/s

Explanation

To find the change in momentum of an object, we can use the formula for momentum, which is given by:

\[ \text{Momentum} (p) = \text{mass} (m) \times \text{velocity} (v) \]

### Step 1: Convert the mass from grams to kilograms
The mass of the object is given as 500 grams. We need to convert this to kilograms because the standard unit of mass in physics is kilograms.

\[ m = 500 \text{ g} = \frac{500}{1000} \text{ kg} = 0.5 \text{ kg} \]

### Step 2: Convert the initial and final speeds to the same unit
The initial speed is given as 200 cm/s and the final speed is given as 0.2 m/s. We should convert the initial speed to meters per second for consistency.

\[ \text{Initial speed} (u) = 200 \text{ cm/s} = \frac{200}{100} \text{ m/s} = 2 \text{ m/s} \]

### Step 3: Calculate the initial momentum
Using the initial speed, we can calculate the initial momentum.

\[ p_{\text{initial}} = m \times u = 0.5 \text{ kg} \times 2 \text{ m/s} = 1 \text{ kg m/s} \]

### Step 4: Calculate the final momentum
Now, we can calculate the final momentum using the final speed.

\[ p_{\text{final}} = m \times v = 0.5 \text{ kg} \times 0.2 \text{ m/s} = 0.1 \text{ kg m/s} \]

### Step 5: Calculate the change in momentum
The change in momentum is given by the difference between the final momentum and the initial momentum.

\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = 0.1 \text{ kg m/s} - 1 \text{ kg m/s} = -0.9 \text{ kg m/s} \]

### Step 6: Interpret the result
The negative sign indicates that the momentum has decreased. Therefore, the change in momentum is:

\[ \Delta p = -0.9 \text{ kg m/s} \]

### Final Answer
The change in momentum is **decreased by 0.9 kg m/s**.

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