# Q. A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c ) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be :

JEE Main JEE Main 2019

Solution:

## Potential at point P, $V = \frac{kQ_{a}}{a} + \frac{kQ_{b}}{b} + \frac{kQ_{c}}{c}$ $\because Q_{a} : Q_{b} : Q_{c} : : a^{2} :b^{2} :c^{2}$ $\left\{\text{since} \sigma_{a} = \sigma_{b} =\sigma_{c}\right\}$ $\therefore Q_{a} = \left[\frac{a^{2}}{a^{2}+b^{2}+c^{2}}\right]Q$ $Q_{b} = \left[\frac{b^{2}}{a^{2}+ b^{2} +c^{2}}\right]Q$ $Q_{c} = \left[\frac{c^{2}}{a^{2}+b^{2} +c^{2}}\right]Q$ $V = \frac{Q}{4 \pi\in_{0}} \left[\frac{\left(a+b+c\right)}{a^{2}+b^{2}+c^{2}}\right]$ $\therefore$ correct answer is (2)

You must select option to get answer and solution

## 1. The increase in pressure required to decrease the 200 L volume of a liquid by 0.004% (in kPa) is (Bulk modulus of the liquid ==2100 MPa)

Maharashtra CET 2006 Mechanical Properties Of Solids

## 2. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

AIPMT 1997 Gravitation

## 3. The diameter of a flywheel is increased by 1%. Increase in its moment of inertia about the central axis is

JIPMER 2015 System Of Particles And Rotational Motion

## 4. There are 26 tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives 3 beats with the next. The first one is octave of the last. What is the frequency of 18th tuning fork?

BHU 2005 Electromagnetic Waves

## 5. A body of mass 4 kg is accelerated upon by a constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is

KCET 2008 Laws Of Motion

## 6. A quarter horse power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be (in erg)

Manipal 2009 Work, Energy And Power

## 7. A cannon of mass I 000 kg, located at the base of an inclined plane fires a shelI of mass 100 kg in a horizontal direction with a velocity 180 $kmh^{-1}$. The angle of inclination of the inclined plane with the horizontal is 45$^{\circ}$. The coefficient of friction between the cannon and the inclined plane is 0.5. The height, in metre, to which the cannon ascends the inclined plane as a result of the recoiI is (g = 10 $ms^{-1})$

EAMCET 2004 Laws Of Motion

## 8. The speed of sound through oxygen at T K is v m$s^{-1}$. As the temperature becomes 2T and oxygen gas dissociates into atomic oxygen, the speed of sound

Manipal 2003 Electromagnetic Waves

## 9. If voltage across a bulb rated 220 volt-100 watt drops by $2.5\%$ of its rated value, the percentage of the rated value by which the power would decrease is

AIPMT 2012 Current Electricity

## 10. Two charges $q_1$ and $q_2$ are placed 30 cm apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius 40cm from C to D. The change in the potential energy of the system is $\frac{q_3}{ 4 \pi \varepsilon_0}$ k. where k is

AIPMT 2005 Electrostatic Potential And Capacitance