If the terminal speed of a sphere of gold (density $= 19.5 \times 10^3 \, kg/m^3$) is $0.2 \, m/s$ in a viscous liquid (density $= 1.5 \times 10^3 \, kg/m^3$),find the terminal speed of a sphere of silver (density $= 10.5 \times 10^3 \, kg/m^3$) of the same size in the same liquid.

When a resistor of $11 \Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \ A$. Instead,when a resistor of $5 \Omega$ is connected to the same electric cell in series,the current increases by $0.4 \ A$. The internal resistance of the cell is (in $\Omega$)

$A$ bucket filled with water is tied to a rope of length $0.5 ~m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is,$(g = 10 ~m/s^2)$.

An electron makes a transition from orbit $n = 4$ to the orbit $n = 2$ of the hydrogen atom. The wave number of the emitted radiation ($R =$ Rydberg's constant) will be

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k=$

When an $AC$ source of $e.m.f. \ e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f. \ e$ and the current $i$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the diagram. If the circuit consists possibly only of $RC$,$RL$,or $LC$ in series,find the relationship between the two elements.