If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would

  • Option 1)


  • Option 2)

    remains unchanged

  • Option 3)


  • Option 4)

    none of these


Answers (1)

As we learnt in 

Percentage decrease in value of 'g' -

\frac{\Delta g}{g}\times 100\: ^{0}\! \! /\! _{0}=\frac{d}{R}\times 100\: ^{0}\! \! /\! _{0}

\Delta g\rightarrow Variation in 'g'

R\rightarrow Radius

g\rightarrow 9.8\, m/s^{2}


- wherein

rate of decrease of gravity outside the earth (h<<R) is double of that of inside the earth.

 g=\frac{GM}{R^{2}}\Rightarrow \frac{dg}{g}=-2\frac{dR}{R}

If  \frac{dR}{R} =-1\%

\Rightarrow \frac{dg}{g} =+2\%

\therefore     g will increase by 2% .

Option 1)


This is incorrect option

Option 2)

remains unchanged

This is incorrect option

Option 3)


This is correct option

Option 4)

none of these

This is incorrect option

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