Two identical charged spheres suspended from a common point by tw… - Vidyadip

MCQ

Two identical charged spheres suspended from a common point by two massless strings of lengths $l,$ are initially at a distance $d\;(d < < l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v.$ Then $v$ varies as a function of the distance $x$ between the spheres, as

A
$v \propto x$
✓
$v \propto {x^{ - \frac{1}{2}}}$
C
$\;v \propto {x^{ - 1}}$
D
$\;v \propto {x^{\frac{1}{2}}}$

✓

Answer

Correct option: B.

$v \propto {x^{ - \frac{1}{2}}}$

b
$\text { From figure, } T \cos \theta=m g.........(i)$

$T \sin \theta=\frac{k q^{2}}{x^{2}}.........(ii)$

From eqns. $(i)$ and $(ii)$, $tan \theta=\frac{k q^{2}}{x^{2} m g}$

since $\theta$ is small, $\therefore \tan \theta \approx \sin \theta = \frac{x}{{2l}}$

$\therefore \quad \frac{x}{2 l}=\frac{k q^{2}}{x^{2} m g} \Rightarrow q^{2}=x^{3} \frac{m g}{2 l k}$ or $q \propto x^{3 / 2}$

$\Rightarrow \frac{d q}{d t} \propto \frac{3}{2} \sqrt{x} \frac{d x}{d t}=\frac{3}{2} \sqrt{x} v$

since, $\frac{d q}{d t}=$ constant

$\therefore v \propto \frac{1}{\sqrt{x}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the track of its centre of mass?

If induction of magnetic field at a point is $B$ and energy density is $U$ then which of the following graphs is correct

A prism of refractive index $\sqrt2$ refracting angle $A$ produces minimum deviation $D_m$ of a ray on one face at an angle of incidence $45^o$ . The values of $A$ and $D_m$ are respectively

A current of $2\, mA$ was passed through an unknown resistor which dissipated a power of $4.4\, W$. Dissipated power when an ideal power supply of $11\, V$ is connected across it is

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of $0.1 \,\,gm/sec$. It melts completely in $100\,\,sec$. The rate of rise of temperature thereafter will be ........$^oC/\sec$ (Assume no loss of heat.)

A long circular tube of length $10 \ m$ and radius $0.3 \ m$ carries a current $I$ along its curved surface as shown. A wire-loop of resistance $0.005$ ohm and of radius $0.1 \ m$ is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $I=I_0 \cos (300 t)$ where $I_0$ is constant. If the magnetic moment of the loop is $N \mu_0 I_0 \sin (300 t)$, then ' $N$ ' is

Consider a hydrogen atom with its electron in the $n ^{\text {th }}$ orbital. An electromagnetic radiation of wavelength $90 \ nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4 \ eV$, then the value of $n$ is ( $hc =1242 \ eV \ nm$ )

Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio

The heat capacity of one mole an ideal is found to be $C_V=3 R(1+a R T) / 2$, where $a$ is a constant. The equation obeyed by this gas during a reversible adiabatic expansion is

Which of the following figure represents the electric field lines due to a single positive charge?