If radius of the earth were to shrink by 1%, its mass remaining the same, g would decrease by nearly

The acceleration due to gravity (g) on Earth's surface is determined by the formula g = GM/R², where G is the gravitational constant, M is the mass, and R is the radius. According to the inverse square law, gravity is inversely proportional to the square of the radius [1]. If the mass remains constant and the radius shrinks by 1% (ΔR/R = -0.01), we can use the differential approximation for small changes: Δg/g = -2(ΔR/R). Substituting the value, Δg/g = -2(-0.01) = +0.02, or a 2% increase. However, the question asks for the magnitude of change or 'decrease' in a context where the phrasing often implies the absolute shift. While g actually increases when the radius shrinks, the numerical magnitude of the change is nearly 2%. This relationship highlights how Earth's shape and radius variations affect gravitational force [1].

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 18: Latitudes and Longitudes > The Shape of The Earth and Latitudinal Heat Zones > p. 241