Electrostatics & Capacitors · JEE Main previous year questions

2010 5 questions

1. Q362010 · 25 Apr 2010 · Shift 1

   Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$, the angle remains the same. If density of the material of the sphere is $1.6\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$, the dielectric constant of the liquid is

   1. A.4
   2. B.3
   3. C.2
   4. D.1
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   Answer: C

2. Q402010 · 25 Apr 2010 · Shift 1
   
   1. A.$\frac{q}{4{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
   2. B.$-\frac{q}{4{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
   3. C.$-\frac{q}{2{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
   4. D.$\frac{q}{2{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
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   Answer: C

3. Q412010 · 25 Apr 2010 · Shift 1

   Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)={\rho }_0\left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r=R$, and $\rho (r)=0$ for $r>R$, where $r$ is the distance from the origin. The electric field at a distance $r$ ($r<R$) from the origin is given by

   1. A.$\frac{{\rho }_{0}r}{4{\epsilon }_0}\left(\frac{5}{3}-\frac{r}{R}\right)$
   2. B.$\frac{4\pi {\rho }_{0}r}{3{\epsilon }_0}\left(\frac{5}{3}-\frac{r}{R}\right)$
   3. C.$\frac{4{\rho }_{0}r}{4{\epsilon }_0}\left(\frac{5}{4}-\frac{r}{R}\right)$
   4. D.$\frac{{\rho }_{0}r}{3{\epsilon }_0}\left(\frac{5}{4}-\frac{r}{R}\right)$
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   Answer: A

4. Q422010 · 25 Apr 2010 · Shift 1

   Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be

   1. A.$1$
   2. B.$\frac{1}{2}$
   3. C.$\frac{1}{4}$
   4. D.$2$
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   Answer: C

5. Q452010 · 25 Apr 2010 · Shift 1

   In a series $LCR$ circuit $R=200\Omega$ and the voltage and the frequency of the main supply are $220\mathrm{V}$ and $50\mathrm{Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ }$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ }$. The power dissipated in the $LCR$ circuit is

   1. A.$305\mathrm{W}$
   2. B.$210\mathrm{W}$
   3. C.zero
   4. D.$242\mathrm{W}$
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   Answer: D