A radioactive nucleus decays as follows :
$$ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 $$
If the mass number and atomic number of ' $X_4$ ' are 172 and 69 respectively, then the atomic number and mass number of ' $X$ ' are
A single slit diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light then
The variation of density of a solid cylindrical rod of cross sectional area $\alpha$ and length $L$ is $\rho=\rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from one end $(x=0)$ is
A simple pendulum is taken at a place where its distance from the earth's surface is equal to the radius of the earth. Calculate the time period of small oscillations if the length of the string is 4.0 m . (Take $g=\pi^2 \mathrm{~ms}^{-2}$ at the surface of the earth.)