Explore topic-wise InterviewSolutions in .

If the potential difference between the plates of a charged and isolated parallel-plate condenser of capacitance 1 μF changes from 12 V to 4 V when a dielectric slab of dielectric constant K is introduced to fill the entire space between the plates, then

At ${40}^{\circ }C$, a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod when it is heated to ${240}^{\circ }C$? The coefficients of linear expansion of brass and steel are $2.0\times {10}^{-5}{}^{\circ }{C}^{-1}$ and $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$ respectively.

A ball of mass m moving horizontally at a speed v collides with the bob of a simple pendulum at rest. The mass of the bob is also m. If the collision is perfectly inelastic, the height to which the two balls
rise after the collision will be given by

If the incident ray given by vector $\overrightarrow{a}=\hat{i}-\hat{j}$, is incident on a plane mirror having its normal along $\hat{j}$, then the unit vector along the reflected ray is given by :

A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale reading has changed from 60 kg to 50 kg for a while and then comes back to the original mark. What should we conclude

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by ${60}^{\circ }$ is $W$. Now the torque required to keep the magnet in this new position is

A long cylindrical shell carries positive surface charge '$\sigma$' in the upper half and negative surface charge '$-\sigma$' in the lower half. The electric field lines around the cylinder will look like

(figures are schematic and not drawn to scale)

A long wire is bent into the shape PQRST as shown in the following figure with QRS being a semicircle with Centre O and radius r meter.
A current of I A flows through it in the direction as shown in the figure. Then the magnetic induction at the point O of the figure in vacuum is:

A current carrying wire (current $=i$) perpendicular to the plane of the paper produces a magnetic field, as shown in the figure. A square of side $a$ is drawn with one of its vertices on the wire. The integral $\int \overrightarrow{B}.\overrightarrow{dr}$ along OPQRO has the value

A and B are concentric circular conductors with center O and carrying currents $I_1$ and $I_2$ as shown in fig. The ratio of their radii is 1: 2 and ratio of their flux densities at O is 1:3 The value of $\frac{I_1}{I_2}$ is

Two particles are in SHM in a straight line about same equilibrium position. Amplitude $A$ and time period $T$ of both the particles are equal. At time $t=0$, one particle is at displacement $y_1=+A$ and the other at $y_2=–A/2$, and they are approaching towards each other. After what time they cross each other ?

Electrons accelerated by voltage $V$ are collimated and used in Young's double slit experiment. Now they are accelerated by voltage $4V$. If initially, fringe width was $\beta$, then new fringe width will be

A particle of mass M is placed at the centre of a uniform spherical shell of mass 2M and radius R. The gravitational potential on the surface of the shell is

A body of mass $m$ is taken from surface of earth to height of $5R$. If gravity at surface is $g_o$, then work done by external force to move the body is (neglect air resistance)

Find $\frac{dy}{dx}$ of $y=\tan x^2$.

A boy wants to climb down a rope. The rope can withstand a maximum tension equal to two-thirds the weight of the boy. If $g$ is the acceleration due to gravity, the minimum acceleration with which the boy should climb down the rope is equal to

Three capacitors connected in series have an effective capacitance of $2\mu \text{F}$. If one of the capacitors is removed, the effective capacitance becomes $3\mu \text{F}$. The capacitance of the capacitor that is removed is

The bob of a simple pendulum of mass m and total energy E will have maximum linear momentum equal to

A portion of length $\pi \text{m}$ is cut out of a conical solid wire. The two ends of this portion have circular cross-sections of radii $r_1=5\text{cm}$ and $r_2=10\text{cm}$. It is connected lengthwise to a circuit and a current $I=2\text{A}$ is flowing through it. The resistivity of the material of the wire is $\rho =1.5\times {10}^{-3}\Omega \text{m}$. Calculate the resistance $R$, of the considered portion and the voltage, $V$ developed across it.

A fixed wedge with both surfaces inclined at ${45}^{\circ }$ to the horizontal is shown in the figure. A block $P$ of mass $m$ is held on the smooth plane by a light string which passes over a smooth pulley A and is attached to a block $Q$ of mass $3m$ which rests on the rough plane. The system is released from rest. Given that the acceleration of each block is of magnitude $\frac{g}{5\sqrt{2}}$ then, the tension in the string is

A body starts from rest and travels a distance $s$ with uniform acceleration, then covers a distance $2s$ uniformly and finally comes to rest after moving further $5s$ distance under uniform retardation. The ratio of the average velocity to maximum velocity is

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4:3$. Effective focal length of the lenses is $+60\text{cm}$, then the focal lengths of the lenses should be

1. 0.45

A sphere of mass $m$ hold at a height $2R$ between a wedge of same mass $m$ and a rigid wall, is released from rest. Assuming that all the surfaces are frictionless. Find the speed of sphere when it hits the ground.

Total kinetic energy of solid sphere of mass $m$ rolling with velocity $v$ without slipping is

A particle of mass m rotates with a uniform angular speed $\omega$. It is viewed from a frame rotating about the Z-axis at a distance a from the particle, with a uniform angular speed ${\omega }_0$. The centrifugal force on the particle is