The acceleration due to earth's gravity on a point particle at a height $h$ above the surface of the earth is denoted by $g_o(h)$ and at a depth $d$ below the surface of the earth is denoted by $g_i(d)$. Consider the earth to be a sphere of radius $R$ with uniform mass density. Which of the following correctly represents the ratio $g_i(d) / g_o(d)$ ?

Consider an infinite one-dimensional wire carrying a uniform current $I$ as shown in the figure. A square loop of side $a$ is initially placed such that the center of the loop is at a distance $R$ from the wire, where $R>\frac{a}{2}$. The square loop is then moved rightwards with a uniform speed as shown in the figure. What is the induced emf in the loop as a function of time $t$ ?