A small steel ball of mass ' M ', radius ' R ' and density ' $\rho$ ' falls with terminal velocity through a tube filled with glycerine of density ' $\sigma$ '. The viscous force acting on the steel ball is ( $\mathrm{g}=$ acceleration due to gravity)
$\mathrm{Mg} \frac{\rho}{\sigma}$
$\mathrm{Mg}(\mathrm{Q}-\sigma)$
$\mathrm{Mg} \rho \sigma$
$M g\left(1-\frac{\sigma}{\rho}\right)$
If the electric flux entering and leaving an enclosed surface area are ' $\phi_1$ ' and ' $\phi_2$ ' respectively, the electric charge inside the surface will be ( $\varepsilon_0=$ permittivity of free space)
$\quad \varepsilon_0\left(\phi_1-\phi_2\right)$
$\quad \varepsilon_0\left(\phi_2-\phi_1\right)$
$\frac{\left(\phi_1+\phi_2\right)}{2}$
$\frac{\left(\phi_1-\phi_2\right)}{2}$
In thermodynamic process, for free expansion, out of the following select the 'WRONG' statement.
Free expansion are adiabatic expansions and there is no exchange of heat between a system and its environment.
There is no work done on the system or by the system.
It is an instantaneous change, and the system is not in thermodynamic equilibrium
A free expansion can be plotted on a p-v diagram.
The frequency of oscillation of LCR series circuit is ' $F$ '. The value of capacitance is tripled, then new frequency becomes ' xF '. The value of ' $x$ ' is
$\sqrt{3}$
$\frac{1}{\sqrt{3}}$
$\frac{1}{6}$
$\frac{1}{\sqrt{6}}$
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