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)

    decrease

  • Option 2)

    remains unchanged

  • Option 3)

    increase

  • 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)

decrease

This is incorrect option

Option 2)

remains unchanged

This is incorrect option

Option 3)

increase

This is correct option

Option 4)

none of these

This is incorrect option

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