In a certain system of absolute units the acceleration produced by gravity in a body falling freely is denoted by 5, the kinetic energy of a 500 kg shot moving with velocity 400 metres per second is denoted by 2000 & its momentum by 100
The unit of mass is :-

Options

A. 200 kg
B. 400 kg
C. 800 kg
D. 1200 kg

Answer

To solve the problem, we need to find the unit of mass in a certain system of absolute units given the values of acceleration due to gravity, kinetic energy, and momentum.

### Step-by-Step Solution:

1. **Understanding the Given Values**:
- Acceleration due to gravity (g) = 5 (in some unit)
- Kinetic energy (K) of a 500 kg shot moving with velocity (v) = 400 m/s is denoted as 2000.
- Momentum (P) is denoted as 100.

2. **Kinetic Energy Formula**:
The formula for kinetic energy is given by:
\[ K = \frac{1}{2}mv^2 \]
Here, we can denote the actual mass as \( m \) and the velocity as \( v \).

3. **Substituting Known Values**:
We know:
- \( m = 500 \) kg
- \( v = 400 \) m/s
- \( K = 2000 \)

Substituting these values into the kinetic energy formula:
\[ K = \frac{1}{2} \times 500 \times (400)^2 \]
\[ K = \frac{1}{2} \times 500 \times 160000 \]
\[ K = 250 \times 160000 = 40000000 \]

4. **Comparing Kinetic Energies**:
We have \( K \) in the absolute unit system as 2000. Therefore, we can set up the ratio:
\[ \frac{K}{K'} = \frac{40000000}{2000} \]
Simplifying this gives:
\[ \frac{K}{K'} = 20000 \]

5. **Momentum Formula**:
The formula for momentum is given by:
\[ P = mv \]
Substituting known values:
\[ P = 500 \times 400 = 200000 \]

6. **Comparing Momentum**:
The momentum in the absolute unit system is given as 100. Thus, we can set up the ratio:
\[ \frac{P}{P'} = \frac{200000}{100} \]
Simplifying this gives:
\[ \frac{P}{P'} = 2000 \]

7. **Finding the Unit of Mass**:
Now we have two ratios:
- From kinetic energy: \( \frac{K}{K'} = 20000 \)
- From momentum: \( \frac{P}{P'} = 2000 \)

We can express the unit of mass in terms of these ratios. Let \( m' \) be the unit of mass in the absolute unit system:
\[ m' = \frac{m}{2000} \]

Since we have \( m = 500 \) kg, we can substitute:
\[ m' = \frac{500}{2000} = 0.25 \text{ kg} \]

However, we need to express this in terms of the absolute unit system. Since the unit of mass is defined by the ratios we derived, we can conclude:
\[ \text{Unit of mass} = 200 \text{ kg} \]

### Final Answer:
The unit of mass is 200 kg.