Question:
How much energy will be necessary for making a body of 500 kg escape from the Earth? (\( g = 9.8 \, \text{m/s}^2 \), radius of the Earth \( = 6.4 \times 10^6 \, \text{m} \))
How much energy will be necessary for making a body of 500 kg escape from the Earth? (\( g = 9.8 \, \text{m/s}^2 \), radius of the Earth \( = 6.4 \times 10^6 \, \text{m} \))
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The energy required for escape from the Earth's surface is the gravitational potential energy calculated using the formula \( E = \frac{GMm}{R} \).
Updated On: Apr 22, 2026
- about 9.8 \( \times 10^6 \) J
- about 6.4 \( \times 10^8 \) J
- about 3.1 \( \times 10^{10} \) J
- about 27.4 \( \times 10^{12} \) J
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The Correct Option is C
Solution and Explanation
Step 1: Use the escape velocity formula.
The energy required for escape is given by the gravitational potential energy required to move the body from the surface to infinity: \[ E = \frac{GMm}{R} \] where,
\( G = 6.67 \times 10^{-11} \, \text{N m}^2 \text{kg}^{-2} \),
\( M = 5.98 \times 10^{24} \, \text{kg} \), \( m = 500 \, \text{kg} \),
and \( R = 6.4 \times 10^6 \, \text{m} \).
Step 2: Substitute values.
Substitute the known values into the formula: \[ E = \frac{6.67 \times 10^{-11} \times 5.98 \times 10^{24} \times 500}{6.4 \times 10^6} \] \[ E \approx 3.1 \times 10^{10} \, \text{J} \]
Step 3: Conclusion.
The required energy is approximately \( 3.1 \times 10^{10} \, \text{J} \), which is option (3).
The energy required for escape is given by the gravitational potential energy required to move the body from the surface to infinity: \[ E = \frac{GMm}{R} \] where,
\( G = 6.67 \times 10^{-11} \, \text{N m}^2 \text{kg}^{-2} \),
\( M = 5.98 \times 10^{24} \, \text{kg} \), \( m = 500 \, \text{kg} \),
and \( R = 6.4 \times 10^6 \, \text{m} \).
Step 2: Substitute values.
Substitute the known values into the formula: \[ E = \frac{6.67 \times 10^{-11} \times 5.98 \times 10^{24} \times 500}{6.4 \times 10^6} \] \[ E \approx 3.1 \times 10^{10} \, \text{J} \]
Step 3: Conclusion.
The required energy is approximately \( 3.1 \times 10^{10} \, \text{J} \), which is option (3).
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