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 $t$ ?

The electric field of an electromagnetic wave is given by $\vec{E}(x, t)=E_0 \hat{z} \cos (a x+b t)$

If $c$ is the speed of light, then the value of $b$ is

An electron of mass $m_e$ has a speed $u_n$ in the $n^{\text {th }}$ Bohr orbit of a hydrogen atom. The normalized speed $V_n$ is given as $V_n=u_n / c=1 / 685$ and the mass of the electron in the units of energy is given as $M_e=m_e c^2=0.51 \times 10^6 \mathrm{eV}$, where $c$ is the velocity of light in a vacuum. It is given that $\frac{e^2}{2 \epsilon_0 h c}=1 / 137$. The Planck's constant h is given as $4.13 \times 10^{-15} \mathrm{eV}-\mathrm{sec}$. The electron makes a transition from $n^{\text {th }}$ orbit to the ground state of the atom. What is the frequency of the emitted photon?