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7.Gravitation
medium
The mass of a spaceship in $1000\,kg$. It is to be launched from the earth's surface out into free space. The value of $'g'$ and $'R'$ (radius of earth) are $10\, m/s^2$ and $6400\, km$ respectively. The required energy of this work will be
A
$6.4\times10^{11}$ Joules
B
$6.4\times10^{8}$ Joules
C
$6.4\times10^{9}$ Joules
D
$6.4\times10^{10}$ Joules
Solution
$\mathrm{W}=0-\left(-\frac{\mathrm{GMm}}{\mathrm{R}}\right)=\frac{\mathrm{GMm}}{\mathrm{R}}$
$=g R^{2} \times \frac{m}{R}=m g R$
$=1000 \times 10 \times 6400 \times 10^{3}$
$=64 \times 10^{9} \mathrm{J}$
$=6.4 \times 10^{10} \mathrm{J}$
Standard 11
Physics
