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Suppose the mass of the earth some how i...

Suppose the mass of the earth some how increases by 10% witout any change in its size. What would happen to your weight? Suppose the radius of the earth becomes twice of its present radius without any change in its mass, what will happen to your weight?

Text Solution

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Case I: Let present mass of earth = M
present radius of earth =R
present acc. Due to gravity =g
present weight =W
mass =m
`:.W=mg`
and `g=(GM)/(R^(2))`
Now `M .=M+10%` of `=+M/10=(11M)/10`
`:.g.=(GM.)/(R^(2))=G/(R^(2))xx(11M)/10`
`=(11GM)/(10R^(2))`
`:.(g.)/g=(11GM)/(10R^(2))xx(R^(2))/(GM)=11/10`
or `g.=11/10g`
Multiplying both sides by m, we get
`mg.=11/10mg`
or `W.=11/10W=1.1W`
Thus our weight will become 1.1 times to our original weight.
Case II: `R.=2R`
`:.g.=(GM)/(R^(.2))=(GM)/((2R)^(2))=(GM)/(4R^(2))`
or `g.=1/4g`
Multiplying both sides by m, we get
`mg.=1/4mg`
or `W.=1/4W`
`:.` Our weight will become one fourth of our original weight.
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