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The mass of a spaceship is . It is to be launched from the earth's surface out into free space. The value of ' ' and ' ' (radius of earth) are and respectively. The required energy for this work will be:

  1. A
    6.4 \times 10^{11} , \text{Joules}
  2. B
    6.4 \times 10^8 , \text{Joules}
  3. C
    6.4 \times 10^9 , \text{Joules}
  4. D
    6.4 \times 10^{10} , \text{Joules}

Solution & Step-by-step Explanation

The energy required to move an object from the surface of the earth to infinity is equal to the change in gravitational potential energy. Since , we have ..

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The mass of a spaceship is . It is to be launched from the earth's surface out into free space. The value of ' ' and ' ' (radius of earth) are and respectively. The required energy for this work will be:
A
6.4 \times 10^{11} , \text{Joules}
B
6.4 \times 10^8 , \text{Joules}
C
6.4 \times 10^9 , \text{Joules}
D
6.4 \times 10^{10} , \text{Joules}

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