Explore topic-wise InterviewSolutions in .

An alternating current is given by $i=i_1\cos \omega t+i_2\sin \omega t$. The rms current is given by

If $\overrightarrow{P}=\overrightarrow{Q}$ then which of the following is NOT correct

Angular acceleration of a circular disc which is initially at rest, about a stationary axis is $\alpha =8\cos 2t$ (in ${\text{rad/s}}^2$). Which of the following graphs correctly represents the variation of angular velocity with respect to time ?

Three charges each of charge ‘q’ are placed at the corners of an equilateral triangle. The fourth charge to be placed at the centre of the triangle so that electrostatic potential energy of the system is zero is

Three blocks $A$, $B$ and $C$ weighing $1$, $8$ and $27\text{kg}$ respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. $T_1$ is equal to $2\text{N}$. Then $T_3$ is

A $2\text{kg}$ body (initially at rest) is displaced by a variable force $F=(3x^2+15)\text{N}$ on a rough horizontal plane with coefficient of kinetic friction $\mu =0.5$. Find the speed of the block, after the block has travelled a distance of $5\text{m}$.

A block of mass $1\text{kg}$ is at rest relative to a smooth wedge moving leftwards with constant acceleration $a=5{\text{ms}}^{-2}.$ Let $N$ be the normal reaction between the block and the wedge. Take $g=10{\text{ms}}^{-2}$. Choose the correct options from the choices given below:

A parallel plate capacitor filled with air has a capacitance of $C$. The distance of separation between the plates is $d$ and the potential difference of $V$ is applied between the plates. Force of attraction between the plates of the parallel plate capacitor is

A drop of liquid of diameter $2.8\text{mm}$ break up into $216$ identical drops. What is the approximate change in energy of bigger drop?

(Given: Surface tension of liquid, $T=75\text{dyne/cm}$)

If a body has a charge of magnitude 8 × 10^–19 coulomb. What is the correct combination of protons and electrons on it?

In a series LCR circuit $R=400\Omega$, $L=7H$ and $C=25\mu F$. The source is V = 200sin(100t). Find the expression for current as a function of time.

An object is displaced from point $A(2,3,4)m$ to a point $B(1,2,3)m$ under the influence of a force $\overrightarrow{F}=2\hat{i}+3y^2\hat{j}+5\hat{k}.$ The workdone by this force is

A particle is thrown vertically upwards. If its velocity at half of the maximum height is $10\frac{m}{s}$, then maximum height attained by it is (Take $g=10\frac{m}{s^2}$)

A steel scale measures the length of a copper wire as $80.0\text{cm}$ when both are at ${20}^{\circ }\text{C}$ (the calibration temperature for the scale). What would be the scale reading for the length of the wire when both are at ${40}^{\circ }\text{C}$? (Given ${\alpha }_{\text{steel}}=11\times {10}^{-6}/{}^{\circ }\text{C}$ and ${\alpha }_{\text{copper}}=17\times {10}^{-6}/{}^{\circ }\text{C})$

A light thread is wound on a disk of mass $m$ and other end of thread is connected to a block of mass $m$, which is placed on a rough ground as shown in diagram. Find the minimum value of coefficient of friction for which block remain at rest.

Two sinusoidal waves produced by two vibrating sources $A$ and $B$ of equal frequencies, are propagating to the point $P$ along a straight line. The amplitude of both of the waves at $P$ is ${}^{\prime }{a}^{\prime }$ and the initial phase of $A$ is ahead by $\frac{\pi }{3}$ than that of $B$. The distance $AP$ is greater than $BP$ by $50\text{cm}$. If the wavelength is $1\text{m},$ then the resultant amplitude at the point $P$ will be

Two cubical blocks of side length $a$ and $2a$ are stuck symmetrically as shown in the figure. The combined block is floating in water with the bigger block just submerged completely. The block is pushed down a little and released. Find the time period of its oscillations. Neglect viscosity.

We have $\overrightarrow{F}=4\hat{i}-3\hat{j}$. Another vector that is perpendicular to $\overrightarrow{F}$ is

How much work should be done in decreasing the volume of an ideal gas by an amount of $2.4\times {10}^{-4}{\text{m}}^3$ at normal temperature and constant pressure of $1\times {10}^5{\text{N/m}}^2$ ?

What will be the equivalent resistance of circuit shown in figure between two points A and D?

A resistor of $16\Omega$ is cut into 4 equal parts. These parts are now connected in parallel. The equivalent resistance of the combination is

Two particles are projected simultaneously with the same speed $v$ in the same vertical plane with angles of elevation $\theta$ and $2\theta$, where $\theta <{45}^{\circ }$. At what time will their velocities be parallel ?

When two tuning forks $A$ and $B$ are sounded together, the number of beats heard is $\nu$. The frequency of fork $A$ is $f$. If the prong of fork $B$ is loaded with a little wax, the number of beats decreases. The initial frequency of fork $B$ is

A small solid sphere of radius $r$ rolls down an incline without slipping which ends into a vertical loop of radius $R$. Find the height above the base so that it just loops the loop.

The ionization potential of the hydrogen atom is $13.6\text{volt}$. The energy required to remove an electron from the second orbit of hydrogen is:

A particle of mass $5\text{kg}$ is initially at rest. A force starts acting on it along a fixed direction. The magnitude of the force changes with time as shown in the figure. Find the velocity of the particle at the end of $20\text{s}$.

The temperature of a gas at pressure $P$ and volume $V$ is ${27}^{\circ }\text{C}$. Keeping its volume constant, if its temperature is raised to ${927}^{\circ }\text{C}$, then its pressure will be -

Six vectors $\overrightarrow{a}$ to $\overrightarrow{f}$ have directions as indicated in the figure. Which of the following statements may be true?

Three point charges q, -2q and -2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be

A constant power $P$ is applied to a particle of mass $m$. The distance travelled by the particle when its velocity increases from $v_1\text{to}{v}_2$ is - (neglect friction)

The position vector of a particle is given as $\overrightarrow{r}=(t^2-4t+6)\hat{i}+\left(t^2\right)\hat{j}.$ The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to

What is the centripetal force acting on a car of weight $15000\text{N}$ moving on a frictionless road banked at an angle of ${30}^{\circ }$?

Two waves are passing simultaneously through a string.

The equation of the waves are given by,

$y_1=A_1\sin k(x-vt)$

and $y_2=A_2\sin k(x-vt+x_0)$

Where the wave number $k=6.28{\text{cm}}^{-1}$ and $x_0=1.50\text{cm}$ The amplitudes are $A_1=5.0\text{mm}$ and $A_2=4.0\text{mm}$. Find the phase difference between the waves and the amplitude of the resulting wave.

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is -

A man running on horizontal road finds the rain falling at angle $\alpha$ with the vertical. If he doubles his speed angle becomes $\beta .$ With what angle with vertical whill rain appear to fall, when he triples his speed? The rain falls vertically down when he is at rest.

A cart of mass $M$ moves with acceleration $a$ as shown in the figure. The minimum force required to hold a block of mass $m$ together is $($friction coefficient between two blocks is $\mu )$

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ respectively from the horizontal, then answer the following questions: If $v_{1}cos{\theta }_1$ = $v_{2}cos{\theta }_2$, then choose the incorrect statement

In the given picture the Ring A at the bottom is positively charged. Another Ring B is brought and placed over it. Ring B hovers at a certain height above A. What could be the charge on Ring B?

Two forces are such that the sum of their magnitudes is $18N$ and their resultant is perpendicular to the smaller force and magnitude of resultant is $12N$. Then the magnitude of the forces are

Figure given below shows a uniform disc of radius $8$ units. A hole of radius $4$ units has been cut out from left of its centre and is placed on the right of the centre of the disc. Find the $COM$ of the resulting shape.

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficient of thermal conductivity $\text{K}$ and $2\text{K}$ and thickness $X$ and $4X$ respectively are $T_2$ and $T_1(T_2>T_1)$. The rate of heat transfer through the slab in a steady state is $\left(\frac{A(T_2-T_1)K}{X}\right)f$, then $f$ is equal to

The energy supply being cut-off, an electric heater element cools down to the temperature of its surroundings, but it will not cool further because

Two identical balls $A$ and $B$ of equal masses, are lying on a smooth surface as shown in figure.





Ball $A$ hits ball $B$ [which is initially at rest] and sticks to it. What should the minimum velocity of ball $A$, so that both balls reach the highest point of inclined place? Ignore the impact at the corner of the inclined surface.

Two cars moving in opposite directions approach each other with speed of $22m/s$ and $16.5m/s$ respectively. The driver of the first car blows a horn having a frequency $400Hz$. The frequency heard by the driver of the second car is (Take velocity of sound $340m/s$)