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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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Increase by $1\%$

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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.Taking the natural logarithm on both sides: $\ln(g) = \ln(G) + \ln(M) - 2\ln(R)$.Differentiating both sides to find the fractional change: $\frac{dg}{g} = \frac{dM}{M} - 2\frac{dR}{R}$.Given that the mass $M$ decreases by $1\%$,so $\frac{dM}{M} = -0.01$.Given that the radius $R$ decreases by $1\%$,so $\frac{dR}{R} = -0.01$.Substituting these values into the equation: $\frac{dg}{g} = (-0.01) - 2(-0.01) = -0.01 + 0.02 = +0.01$.This represents an increase of $1\%$ in the value of $g$.

If both the mass and the radius of the earth decrease by $1\%$,the value of the acceleration due to gravity will

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