Physics, asked by anku53, 1 year ago

if radius of earth shrinks by 2 % mass remaining same, how much will be the change in value of g?

Answers

Answered by Bhaavya1
0
1.04 times...

plzz mark it as a brainliest answer
Attachments:
Answered by TheVang51
1

\huge\bold{Solution}

◆Let M, R be the mass and radius of earth.The acceleration due to gravity on the surface of Earth is given by

g = \frac{GM}{R {}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .........(1)

●Differentiating it, we have

dg = - \frac{2GM}{R {}^{3} }dR \: \: \: \: \: \: \: \: \: \: .......(2)

●Dividing (2) by (1), we have,

 \frac{dg}{g} = - \frac{2dR}{R}

●When radius of Earth shrinks by 2% then,

 \frac{dR}{R} = - \frac{2}{100}

●From (1) & (2) , the percentage increase in the value of "g" is =

 \frac{dg}{g} \times 100 = - \frac{2dR}{T} \times 100 = - 2( \frac{ - 2}{100} \times 100) \\ \\ = 4\%

◆Hence the value of acceleration due to gravity change by 4%.

Similar questions