A particle performs S.H.M. with amplitude 'A'. The speed of the particle is $\left(\frac{1}{3}\right)^{\text {rd }}$ of the maximum speed when its displacement from the mean position is
$\frac{\mathrm{A}}{3}$
$\frac{\sqrt{2} \mathrm{~A}}{3}$
$\frac{2 \sqrt{2} \mathrm{~A}}{3}$
$\frac{2 \mathrm{~A}}{3}$
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)
$[2 \mathrm{gR}(\mathrm{r}-\mathrm{R}) / \mathrm{r}]^{\frac{1}{2}}$
$\left[g R(r-R) / r^2\right]^{\frac{1}{2}}$
$\quad\left[2 \mathrm{gR}(\mathrm{r}-\mathrm{R}) / \mathrm{r}^2\right]^{\frac{1}{2}}$
$\left[g R^2(r-R) / r^2\right]^{\frac{1}{2}}$
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