If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

<p>The acceleration due to gravity (g) on the surface of a planet is given by the formula:</p> <p>$g = \frac{G M}{R^2}$</p> <p>where:</p> <ul> <li>G is the gravitational constant,</li> <li>M is the mass of the planet,</li> <li>R is the radius of the planet.</li> </ul> <p>If the radius of the Earth shrinks by 2% but its mass remains the same, the new acceleration due to gravity (g&#39;) will be:</p> <p>$g&#39; = \frac{G M}{(0.98R)^2} = \frac{G M}{0.9604 R^2} = \frac{g}{0.9604}$</p> <p>This implies that g&#39; is approximately 1.0412 times g, or an increase of approximately 4.12%.</p> <p>Therefore, the acceleration due to gravity on the Earth&#39;s surface will approximately increase by 4%. </p>