If the rate of emission of energy from a star is `2.7 xx 10^(36)` J/ sec, the rate of loss of mass in the star will be

Options

A. (a)`3xx10^(18) kg//sec`
B. (b)`3xx10^(19) kg//sec`
C. (c)`3xx10^(20) kg//sec`
D. (d)`3xx10^(21) kg//sec`

Answer

To find the rate of loss of mass in the star given the rate of emission of energy, we can use Einstein's mass-energy equivalence principle, which is expressed by the equation:

\[ E = mc^2 \]

Where:
- \( E \) is the energy,
- \( m \) is the mass,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Rate of emission of energy, \( \frac{dE}{dt} = 2.7 \times 10^{36} \) J/s.
- Speed of light, \( c = 3 \times 10^8 \) m/s.

2. **Differentiate the Energy-Mass Relation**:
- From the equation \( E = mc^2 \), differentiate both sides with respect to time \( t \):
\[ \frac{dE}{dt} = c^2 \frac{dm}{dt} \]
Here, \( \frac{dm}{dt} \) represents the rate of loss of mass.

3. **Rearrange the Equation to Solve for \( \frac{dm}{dt} \)**:
\[ \frac{dm}{dt} = \frac{1}{c^2} \frac{dE}{dt} \]

4. **Substitute the Known Values**:
- Substitute \( \frac{dE}{dt} \) and \( c \) into the equation:
\[ \frac{dm}{dt} = \frac{2.7 \times 10^{36}}{(3 \times 10^8)^2} \]

5. **Calculate \( c^2 \)**:
- Calculate \( (3 \times 10^8)^2 \):
\[ (3 \times 10^8)^2 = 9 \times 10^{16} \]

6. **Substitute \( c^2 \) Back into the Equation**:
\[ \frac{dm}{dt} = \frac{2.7 \times 10^{36}}{9 \times 10^{16}} \]

7. **Perform the Division**:
- Simplify the expression:
\[ \frac{dm}{dt} = \frac{2.7}{9} \times 10^{36 - 16} = 0.3 \times 10^{20} = 3 \times 10^{19} \text{ kg/s} \]

8. **Final Result**:
- The rate of loss of mass in the star is:
\[ \frac{dm}{dt} = 3 \times 10^{19} \text{ kg/s} \]

### Conclusion:
The rate of loss of mass in the star is \( 3 \times 10^{19} \) kg/s.