At what temperature is the root mean square rms speed of neon gas atoms is equal to the rms speed of helium gas atoms at $-33^{\circ} \mathrm{C}$ ?

(Atomic mass of $\mathrm{Ne}=20.2 \mathrm{u}$, and that of $\mathrm{He}=4.0 \mathrm{u}$ )

A wire of length 0.4 m stretched at both ends vibrates 250 times per second. If the length of the wire is increased by 0.1 m and the stretching force is reduced to $1 / 4$ th of its original value, then the new frequency is

A spherical glass is attached to a rigid wall as shown in the figure. An observer located at point $O$ is looking at a point $A$ on the wall. The refractive index of the glass is 1.5 and that of air is 1.0 . The distances are $O A=8 \mathrm{~cm}$, $X A=3 \mathrm{~cm}$. If the radius of curvature of spherical glass surface is $R=5 \mathrm{~cm}$, then the apparent distance of $A$ from observer $O$ is

In a double slit experiment performed in air, the angular width of a fringe is found to be $0.15^{\circ}$ on a screen placed 80 cm away. The wavelength of light is used 490 nm . The angular width of the fringe, if the entire apparatus is immersed in a medium of refractive index $\frac{5}{3}$ is