In the Bohr model of hydrogen atom, out of the following quantities, the principal quantum number is proportional to ( $\mathrm{R}, \mathrm{V}$ and E represent radius of the orbit, speed of electron and total energy of the electron respectively)
$\frac{\mathrm{V}}{\mathrm{R}}$
VR
$\frac{E}{V}$
$\frac{E}{R}$
An open organ pipe and a closed organ pipe have the frequency of their second overtone identical. The ratio of length of closed pipe to that of open pipe is (Neglect end correction)
$2: 3$
$5: 6$
$3: 4$
$6: 7$
An object is released from a distance ' $r$ ' from the centre of the earth. The velocity of the object at the time of striking the earth will be ( $R=$ radius of earth, $r>R, g=$ acceleration due to gravity)
$[2 \mathrm{gR}(\mathrm{r}-\mathrm{R}) / \mathrm{r}]^{\frac{1}{2}}$
$\left[g R(r-R) / r^2\right]^{\frac{1}{2}}$
$\quad\left[2 \mathrm{gR}(\mathrm{r}-\mathrm{R}) / \mathrm{r}^2\right]^{\frac{1}{2}}$
$\left[g R^2(r-R) / r^2\right]^{\frac{1}{2}}$
According to Bohr's first postulate the kinetic energy $\frac{1}{2} m v^2$ of the electron in C.G.S. system is ( $\mathrm{m}=$ mass of electron, v is its velocity, r is the radius of the stationary orbit around the nucleus with charge Ze )
$\frac{\mathrm{Ze}}{\mathrm{r}^2}$
$\frac{\mathrm{Ze}^2}{\mathrm{r}}$
$\frac{\mathrm{Ze}^2}{2 \mathrm{r}}$
$\frac{\mathrm{Ze}^2}{2 \mathrm{r}^2}$
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