In a certain system of absolute units the acceleration produced by gravity in a body falling freely is denoted by `3`, the kinetic energy of a `272.1 kg` shot moving with velocity `448` metres per second is denoted by `100`, and its momentum by 10.
the unit of mass is

Options

A. 544.2 kg
B. 54.42 kg
C. 5442 kg
D. None of these

Explanation

To find the unit of mass in the given system, we will follow these steps:

### Step 1: Understand the given quantities
We know:
- The acceleration due to gravity is denoted by `3`.
- The kinetic energy of a shot moving with velocity `448 m/s` is denoted by `100`.
- The momentum of the shot is denoted by `10`.
- The mass of the shot in the conventional system is `272.1 kg`.

### Step 2: Write the equations for kinetic energy and momentum
1. **Kinetic Energy (KE)** is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
In the new system, this is denoted as:
\[ \frac{1}{2} m' v'^2 = 100 \quad \text{(Equation 1)} \]

2. **Momentum (p)** is given by the formula:
\[ p = mv \]
In the new system, this is denoted as:
\[ m' v' = 10 \quad \text{(Equation 2)} \]

### Step 3: Solve for \( v' \)
From Equation 2, we can express \( v' \):
\[ v' = \frac{10}{m'} \]

### Step 4: Substitute \( v' \) into the kinetic energy equation
Substituting \( v' \) from Equation 2 into Equation 1:
\[ \frac{1}{2} m' \left(\frac{10}{m'}\right)^2 = 100 \]
This simplifies to:
\[ \frac{1}{2} m' \cdot \frac{100}{(m')^2} = 100 \]
\[ \frac{50}{m'} = 100 \]
Now, solving for \( m' \):
\[ m' = \frac{50}{100} = 0.5 \]

### Step 5: Relate \( m' \) to the conventional mass
From the problem, we know that the mass of the shot in the conventional system is \( 272.1 kg \). Therefore, we can set up the relationship:
\[ m' = 0.5 \times m_{unit} \]
Where \( m_{unit} \) is the unit of mass in the new system.

### Step 6: Solve for the unit of mass
We can express this as:
\[ 0.5 \times m_{unit} = 272.1 \]
Thus,
\[ m_{unit} = \frac{272.1}{0.5} = 544.2 \]

### Conclusion
The unit of mass in the given system is:
\[ \text{Unit of mass} = 544.2 \text{ kg} \]