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(B) The acceleration due to gravity $g$ is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the ea

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Will increase

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(B) The acceleration due to gravity $g$ is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the earth,and $R$ is the radius of the earth.From this,we see that $g \propto \frac{1}{R^2}$.Given that the radius $R$ decreases by $2\%$,we can use the approximation for small changes: $\frac{\Delta g}{g} \approx -2 \frac{\Delta R}{R}$.Since $\frac{\Delta R}{R} = -0.02$,the change in $g$ is $\frac{\Delta g}{g} \approx -2(-0.02) = 0.04$ or $4\%$.Since $g$ increases,the weight of the body $W = mg$ will also increase by $4\%$.

If the radius of the earth contracts by $2\%$ and its mass remains the same,then the weight of a body at the earth's surface:

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