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

We need to find the percentage change in acceleration due to gravity when the radius of Earth shrinks by 2% while mass remains constant. Using the relation

$$g = \frac{GM}{R^2}$$

and taking its differential yields

$$\frac{\Delta g}{g} = -2\frac{\Delta R}{R}.$$

Since the radius decreases by 2%, i.e., $$\frac{\Delta R}{R} = -2\%,$$ it follows that

$$\frac{\Delta g}{g} = -2 \times (-2\%) = +4\%.$$

Equivalently, because $$g \propto \frac{1}{R^2},$$ a reduction in R increases g, so a 2% decrease in the radius brings about approximately a 4% increase in g. Hence, the correct answer is Option D: increase by 4%.