MCQ
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be

(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )

  • A
    $4$
  • B
    $8$
  • C
    $7$
  • $3$

Answer

Correct option: D.
$3$
d
In air $\tan \frac{\theta}{2}=\frac{F}{m g}=\frac{q^2}{4 \pi \varepsilon_0 \mathrm{r}^2 m g}$

In water $\tan \frac{\theta}{2}=\frac{\mathrm{F}^{\prime}}{\mathrm{mg}^{\prime}}=\frac{\mathrm{q}^2}{4 \pi \varepsilon_0 \varepsilon_{\mathrm{r}} \mathrm{r}^2 \mathrm{mg}_{\text {eff }}}$

Equate both equations

$\varepsilon_0 g=\varepsilon_0 \varepsilon_{\mathrm{r}} \mathrm{g}\left[1-\frac{1}{1.5}\right]$

$\varepsilon_{\mathrm{T}}=3$

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

Similar questions

The solar constant on the surface of the earth is S. What will be its value on the surface of another planet which is about 5.3 A.U. away from sun
A rod AB moves with a uniform velocity v in a uniform magnetic field as shown in figure:
Image
As the switch $S$ is closed in the circuit shown in figure, current passed through it is .................. $A$
The electric field in a region is given by $\overrightarrow{ E }=\frac{2}{5} E _{0} \hat{ i }+\frac{3}{5} E _{0} \hat{ j }$ with $E _{0}=4.0 \times 10^{3}\, \frac{ N }{ C } .$ The flux of this field through a rectangular surface area $0.4 \,m ^{2}$ parallel to the $Y - Z$ plane is ....... $Nm ^{2} C ^{-1}$
A student studying the similarities and differences between a camera and the human eye makes the following observations:

$I$. Both the eye and the camera have convex lenses.

$II$. In order to focus, the eye lens expands or contracts while the camera lens moves forward or backward.

$III$. The camera lens produces upside down real images while the eye lens produces only upright real images.

$IV$. A screen in camera is equivalent to the retina in the eyes.

$V$. A camera adjusts the amount of light entering in it by adjusting the aperture of the lens. In the eye, the cornea controls the amount of light. Which of the above statements are correct?

A thin rod of length$f/3$ lies along the axis of a concave mirror of focal length $f.$ One end of its magnified image touches an end of the rod. The magnification of the image is
A nucleus ruptures into two nuclear parts which have their velocity ratio equal to $2: 1$. What will be the ratio of their nuclear size (nuclear radius)
Kinetic energy with which the electrons are emitted from the metal surface due to photoelectric effect is
When a thin transparent plate of thickness t and refractive index m is placed in the path of one of the two interfering waves of light, then the path difference changes by 
A rectangular loop has a sliding connector $PQ$ of length $2\ m$ and resistance $10\ \Omega  $  and it is moving with a speed $5\ m/s$ as shown. The set-up is placed in a uniform magnetic field $3\ T$ going into the plane of the paper. The three currents $I_1$ , $I_2$ and $I$ are