Explore topic-wise InterviewSolutions in Current Affairs.

Excess pressure inside a soap bubble is '$a$', if radius of bubble is '$b$' & surface tension is '$c$', then which of the following is dimensionless?

An infinite line charge produces a field of $9\times {10}^{4}N/C$ at a distance of 2cm. Calculate the linear charge density.

A ball of mass $m$ is moving with a velocity $v$ towards a rigid vertical wall. After striking the wall, the ball gets deflected by an angle $\theta$ without any change in its speed. The impulse imparted to the ball will be

The plot of velocity versus time graph for a particle moving along a straight line is shown.

The value of dot product of velocity and acceleration of particle at $t=2s$ is

What is the value of linear velocity, if$\overrightarrow{\omega }=3\hat{i}-4\hat{j}+\hat{k}$ and $\overrightarrow{r}=5\hat{i}-6\hat{j}+6\hat{k}$? [Hint: linear velocity $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$]

Two plane mirrors are inclined at an angle $\theta$ as shown in the figure. Find the value of $\theta$ such that the light ray retraces its path after second reflection.

A vessel is filled with a gas at a pressure of $76\text{cm}$ of mercury at a certain temperature. The mass of the gas is increased by $50\%$ by introducing more gas in the vessel at the same temperature. The resultant pressure, in cm of $Hg$, is -

Evaluate $\int x^2\sin xdx$

A block of mass $m$ is placed on a surface which is a locus of the equation $Y=2x^2$, where $Y$ is along the vertical direction and $x$ is along the horizontal direction. If coefficient of friction is 0.5, then maximum height above the ground at which the block can be placed without slipping is

A particle of $4kg$ has an initial velocity of $3\hat{i}+4\hat{j}$. It is pushed by force $a\hat{i}+b\hat{j}$, and after sometime velocity becomes $7\hat{i}+24\hat{j}$. Then the work done by force during the interval is

In a series $CR$ circuit shown in figure, the applied voltage is $10V$ and the voltage across capacitor is found to be $8V$. If the voltage across $R$ and the phase difference between current and the applied voltage respectively be $x$ and ${\tan }^{-1}\left(y\right)$, then the value of $\frac{2x}{y}$ is

In figure, a square loop consisting of an inductor of inductance L and resistor of resistance R is placed between two long parallel wires. The two long straight wires have time varying current of magnitude
$I=I_{0}cos\omega t$ but the direction of current in them are opposite.

Magnitude of emf in this circuit only due to flux change associated with two long straight current carrying wires will be

A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $r$ and angular velocity of the rotation is $\omega$, then the difference in the heights of the liquid at the center of the vessel and the edge is

A uniform rod of mass m and length l₀ is pivoted at one end and is hanging in the vertical direction. The period of small angular oscillations of the rod is

A force $\overrightarrow{F}$ = $k[k\hat{i}+y\hat{j}]$ , where k is a positive constant, acts on a particle moving in x-y plane starting from the point (3,5), the particle is taken along a straight line to (5, 7). The work done by the force is :

A ray of light incident on the first mirror parallel to the second and is reflected from the second mirror parallel to first mirror. The angle between two mirrors is

Two polaroids are crossed to each other. When one of them is rotated through ${60}^{\circ }$, then what percentage of the incident unpolarised light will be transmitted by the polaroids?

The magnetic field energy in an inductor changes from maximum value to minimum value in 5 ms when connected to an AC source. The frequency of the source is

Two block of mass $m_A=10\text{kg}$ and $m_B=15\text{kg}$ are connected by a light inextensible string and placed on a smooth horizontal surface as shown in the figure. Find the value of tension force on block $A$, if force applied on block $B$ is $50\sqrt{3}\text{N}$ .

In an arrangement shown in the figure, the mass of $A=1\text{kg}$, the mass of $B=2\text{kg}$, and coefficient of friction between $A$ and $B$ is $0.2$. There is no friction between $B$ and the ground. The frictional force on $A$ is (Take $g=10{\text{m/s}}^2$)

(Assume there is no slipping between the blocks).

A particle has potential energy dependent on its position on the $x$ axis, represented by the function $U\left(x\right)=e^{2x}+1$ for all real values of $x$, where $U\left(x\right)$ and $x$ are given in standard units. The force it feels at position $x=1$ is closest to
[Take $e=2.72$]

Who among the following is seated exactly between B and D?

A car, starting from rest, is accelerated at a constant rate $\alpha$ until it attains a speed $v$. It is then retarded at a constant rate $\beta$ until it comes to rest. The average speed of the car during its entire journey is

A ball of mass 'm', moving with a velocity 'v' along X-axis, strikes another ball of mass '2m' kept at rest. The first ball comes to rest after collision and the other breaks into two equal pieces. One of the pieces starts moving along Y-axis with a speed $v_1$. What will be the velocity of the other piece?

What is the velocity of block B?

Three identical sperical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is:

The formal charge on oxygen which is single bonded in ozone is:

A monkey of mass $12\text{kg}$ climbs up a light rope as shown in figure. The rope passes over a light and frictionless pulley and it is attached to a bunch of bananas having mass $16\text{kg}$. What will be maximum acceleration of monkey without lifting the bunch of bananas? (Take $g=10{\text{m/s}}^2$)

A rocket has a mass of 100 kg. $90\%$ of this is fuel. It ejects fuel vapours at therate of 1 kg/sec with a velocity of 500 m/sec relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is

A wagon weighing 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is

A particle moving along a circle has velocity $\overrightarrow{v}=2\hat{i}+3\hat{j}+5\hat{k}m/s$ and angular velocity $\overrightarrow{\omega }=2\hat{i}+2\hat{j}-2\hat{k}$, at a particular instant. The magnitude of centripetal acceleration of the particle is

If frame of reference is changed, which quantity may change its value ?

The work done in increasing the potential of a capacitor from $V$ volt to $2V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor from $2V$ volt to $4V$ volt will be

A particle moves from A to B along a semicircle of radius 1.0m in 1s. Magnitude of the average velocity would be

A solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane of height $h$. The angular velocity of the cylinder when it reaches the bottom of the plane will be

P,Q and R are in partnership sharing profits and losses in the ratio of 3:2:1. They decided to admint S into partnership with 1/8th share which he acquire form P and R equally, At the date of admission S will bring Rs 50,000 as his capital and his share of goodwill in cash Goodwill is to be valued at 3 years purchase of average profits of last 4 years or 5 years whichever is more. Profits were as Rs 20,000, Rs 30,000,Rs 40,000, Rs 70,000 and Rs 65,000. Pass necessary Journal entries and show the working clearly and also find the sacrificing ratio and new ratio.

A system of coordinates is drawn in a medium whose refractive index varies as $\mu =\frac{2}{1+y^2}$, where $0\le y\le 1$ and $\mu =2$ for $y<0$ as shown in figure. A ray of light is incident at origin at an angle ${60}^{\circ }$ with y - axis as shown in the figure. At point $P$, ray becomes parallel to x - axis. The value of $H$ is:-

The pressure and density of a diatomic gas $(\gamma =\frac{7}{5})$ change adiabatically from (p,d) to (p',d'). If $\frac{d^{\prime }}{d}=32$, then $\frac{P^{\prime }}{P}$ should be.

Stationary waves are formed when

[NCERT 1983]

Two blocks of masses 40 kg and 20 kg are connected by a wire that has a linear mass density of 1 g/m. These blocks are being pulled across horizontal frictionless floor by horizontal force F that is applied to 20 kg block. A transverse wave travels on the wave between the blocks with a speed of 400 m/s (relative to the wire). The mass of the wire is negligible compared to the mass of the blocks. The magnitude of F is

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are at right angles to each other , when

Calculate the number of states per cubic metre of sodium in 3s band. The density of sodium is $1013kg{m}^{-3}.$ How many of them are empty ?

The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$ is (R = radius of the earth)

Light falls from glass $(\mu =1.50)$ to air. Find the angle of incidence for which the angle of deviation is ${90}^{\circ }$.

A pin of length 2.00 cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1.00 cm is formed at a distance of 40.0 cm from the pin. Find the focal length of the lens and its distance from the pin.