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2 months, 3 weeks ago

# The radius and mass of earth are increased by

The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth? A) g will increase B)             g will decrease C)             Escape velocity will remain unchanged D)             Potential energy will remain unchanged
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V Vishwash Tetarwal
Answered 2 months, 3 weeks ago

$g = \frac{GM}{{R}^{2}}$

${v}_{e} = \sqrt{\frac{2GM}{R}}$

$U=\frac{-GMm}{R}$

$g\propto \frac{M}{{{R}^{2}}}$

${{v}_{e}}\propto \sqrt{\frac{M}{R}}$

$U\propto \frac{M}{R}$

after increasing by 0.5%

$M_{new} = M+(0.5/100)M=1.005M$

$R_{new} = R+(0.5/100)R=1.005R$

So If both mass and radius are increased by 0.5% then $v_{e}$ and U remains unchanged where as g will be decreased.

V Vishwash Tetarwal
Answered 2 months, 3 weeks ago

$g = \frac{GM}{{R}^{2}}$

${v}_{e} = \sqrt{\frac{2GM}{R}}$

$U=\frac{-GMm}{R}$

$g\propto \frac{M}{{{R}^{2}}}$

${{v}_{e}}\propto \sqrt{\frac{M}{R}}$

$U\propto \frac{M}{R}$

after increasing by 0.5%

$M_{new} = M+(0.5/100)M=1.005M$

$R_{new} = R+(0.5/100)R=1.005R$

So If both mass and radius are increased by 0.5% then $v_{e}$ and U remains unchanged where as g will be decreased.

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