COMEDK202510 May 2025Evening ShiftPhysicsNuclear PhysicsActual
To get 300 MW electric power for half an hour, how much mass is to be completely converted into energy?
Options
- A3 10⁻⁶ ~kg
- B6 10⁻⁶ ~kg
- C6 10⁻² ~kg
- D6 10⁻³ ~kg
Correct answer
B. 6 10⁻⁶ ~kg
Step-by-step solution
The total energy E required is given by the product of power P and time t . P = 300 MW = 300 10⁶ W t = 30 minutes = 30 60 seconds = 1800 s E = P t = 300 10⁶ 1800 = 540000 10⁶ = 5.4 10¹¹ J Using Einstein mass-energy equivalence relation E = mc² , where c = 3 10⁸ m/s is the speed of light: m = E c² = 5.4 10¹¹ (3 10⁸)² m = 5.4 10¹¹ 9 10¹⁶ m = 0.6 10⁻⁵ kg = 6 10⁻⁶ kg Answer: 6 10⁻⁶ ~kg