Question

The mass of a spaceship is $1000\text{kg}$. It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth) are $10{\text{m/s}}^2$ and $6400\text{Km}$ respectively. The required energy for this work will be

• A. $6.4\times {10}^9$ $\text{J}$
• B. $6.4\times {10}^8$ $\text{J}$
• C. $6.4\times {10}^{10}$ $\text{J}$
• D. $6.4\times {10}^{11}$ $\text{J}$

Answer 1

The correct option is C $6.4\times {10}^{10}$ $\text{J}$

Potential energy on earth surface is - $mgR$ while in free space it is zero.
So, to free the spaceship, minimum required energy is
$E=mgR={10}^3\times 10\times 6400\times {10}^3$
$=6.4\times {10}^{10}$ $\text{J}$
Hence, option $\left(D\right)$ is correct.