If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would

Step-by-step solution

The acceleration due to gravity g on the surface of the earth is given by the formula g = GM R^2 , where G is the gravitational constant, M is the mass of the earth, and R is the radius of the earth. Given that the mass M remains constant, g is inversely proportional to the square of the radius, g R⁻² . Taking the logarithmic derivative of the relation g = GM R⁻² , we get dg g = -2 dR R . The radius shrinks by two percent, which means dR R = -0.02 . Substituting this value into the expression for the fractional cha