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Engineering
1 week, 6 days 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
Answers (2)
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V Vishwash Tetarwal
Answered 1 week, 3 days 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 1 week, 3 days 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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