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7. gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
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
  • ✓
    $6.4\times10^{10}$ Joules
✓

Answer

Correct option: D.
$6.4\times10^{10}$ Joules
d
$\mathrm{W}=0-\left(-\frac{\mathrm{GMm}}{\mathrm{R}}\right)=\frac{\mathrm{GMm}}{\mathrm{R}}$

$=g R^{2} \times \frac{m}{R}=m g R$

$=1000 \times 10 \times 6400 \times 10^{3}$

$=64 \times 10^{9} \mathrm{J}$

$=6.4 \times 10^{10} \mathrm{J}$

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