Explore topic-wise InterviewSolutions in .

The variation of electric potential $\left(V\right)$ with distance $\left(r\right)$ from a fixed point is as shown in the figure. Electric field intensity $(\text{in V/m)}$ at $r=1\text{m},3\text{m}$ and $4.5\text{m}$ are respectively

The time period of oscillation of a mass suspended by a spring (force constant k) is T. If the spring is cut into three equal pieces, the force constant of each part and the periodic time, if the same mass is suspended from one piece are

Show that each of the given three vectors is a unit vector:
$\frac{1}{7}(2\hat{i}+3\hat{j}+6\hat{k}),\frac{1}{7}(3\hat{i}-6\hat{j}+2\hat{k}),\frac{1}{7}(6\hat{i}+2\hat{j}-3\hat{k})$. Also, show that they are mutually perpendicular to each other.

A rod of mass $m$ and length $L$, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed $v$ strikes the rod horiozontally at a distance $x$ from its pivoted end and gets embedded in it. The combined system now rotates with angular speed $\omega$ about the pivot. The maximum angular speed ${\omega }_m$ is achieved for $x=x_m$. Then:

A prism having refractive index $\sqrt{2}$ and refracting angle ${30}^{\circ }$, has one of the refracting surface polished. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is :

A boy brings the palm of his hand near the disc of a charged gold leaf electroscope. the leaves of the electroscope are observed to collapse slightly. But when the boy his hand away from the gold leaf electroscope leaves resume their original position.how do you explain the behaviour of leaves?

The magnetic field at center, $P$ will be

Design rate of superelevation for horizontal highway curve of radius 450 m for a mixed traffic condition, having a speed of 125 km/hour is

A block of mass 5.0 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below so that it acquired an upward speed of 2.0 m/s . How high will it rise?

A prism $(\mu =1.5)$ has the refracting angle of ${30}^{\circ }$. The deviation of a monochromatic ray incident normally on its one surface will be $(sin{48}^{\circ }{36}^{\prime }=0.75)$

The equation of a stationary wave is $y=0.8\text{cos}\left(\frac{\pi x}{20}\right)\text{sin}200\pi t$, where $x$ is in $\text{cm}$ and $t$ is in seconds. The separation between a successive node and antinode will be

A thin spherical shell of mass $M$ and radius $R$ as shown in the figure slips on a rough horizontal plane. At the same instant, it has translational velocity $v_0$ and rotational velocity about the centre $\frac{3v_0}{R}$ . Find the translation velocity after the shell starts pure rolling.

Two mirrors 1 and 2 are kept parallel to each other as shown, with their reflecting surfaces facing each other. If the angle of incidence of a ray on mirror 1 is 40°, what will be the angle of reflection from mirror 2?

A lamp consumes only $50\%$ of peak power in an ac circuit. What is the phase difference between the applied voltage and the circuit current

Pressure is exerted by a gas on the walls of the container because

A horizontal rope of $1\text{m}$ length, having a mass $100\text{g}$, is fixed at one end and is tied to a light string at the other end. Find the frequency and wavelength of the fifth overtone, if the tension in the string is $40\text{N}$.

An rms voltage of $110\text{V}$ is applied across a series circuit having a resistance $11\Omega$ and an impedance $22\Omega$. The power consumed is

The elevator shown in figure is descending with an acceleration of $2{\text{m/s}}^2$. The mass of the block $A=0.5\text{kg}$. The magnitude of force exerted by the block $A$ on block $B$ is

Which impurity is doped in Si to form N-type semi-conductor?

The optical path of a monochromatic light is the same, when it goes either through $2.00\text{cm}$ of glass or $2.25\text{cm}$ of water. If, the refractive index of water is $1.33$, what is the refractive index of glass?

A closed cubical box is completely filled with water and is accelerated horizontally towards right with constant acceleration a. The resultant normal force by the water on the top of the box.

Find current passing through the battery.

A bob of mass $m$ suspended by a length $l$ undergoes simple harmonic oscillations with time period $T$. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the threat is increased by $(1/3{)}^{rd}$ of the original length, then the time period of the simple harmonic oscillation will be

Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right-hand vessel(s = relative density of mercury and $\rho$ = density of water) by

The moment of inertia of a hollow cylinder of radius $R$ and mass $M$ about an axis passing through the outer circumference along the height of the hollow cylinder is

A car has an initial velocity of $100\text{m/s}$. On the application of brakes the car stops at $200\text{m}$. The acceleration of the car will be

A box weighing $2000N$ is to be slowly slid through $20m$ on a straight track having friction coefficient $0.2$ with the box. Find the work done by the person pulling the box with a chain at an angle $\theta$ with the horizontal.