Explore topic-wise InterviewSolutions in Current Affairs.

Find the most probable speed $\left(V_{mp}\right)$ of nitrogen gas molecules at $T=560\text{K}$. (Given: $\sqrt{R}=2.88$, where $R$ is gas constant)

A van of mass 1500 kg travelling at a speed of 54 km $h^{-1}$ is stopped in 10 s. Assuming that all the mechanical energy lost appears as thermal energy in the brake mechanism, find the average rate of production of thermal energy in cal $s^{-1}$.

A thin paper of thickness 0.02 mm having a refractive index 1.45 is pasted across one of the slits in a young's double slit experiment. The paper transmits $\frac{4}{9}$ of the light energy falling on it. (a) Find the rationof te maximum intensity to the minimum intensity in the fringe pattern. (b) how many fringes will cross through the centre if an identical paper piece is pasted on the other slit also, The wavelength of the light used is 600 nm.

An unloaded bus and a loaded bus are both moving with the same kinetic energy. The mass of the latter is twice that of the former. Brakes are applied to both, so as to exert equal retarding force. If $x_1$and $x_2$ be the distance covered by the two buses respectively before coming to a stop, then

When the electrical conductivity of a semi- conductor is due to the breaking of its covalent bonds, then the semiconductor is said to be

Column Matching:



$$\begin{array}{cc}\text{Column (I)}& \text{Column (II)}\\ \begin{array}{cc}\text{(A)}& \text{In}{R}^2,\text{if the magnitude of the projection}\\ & \text{vector of the vector}\alpha \hat{i}+\beta \hat{j}\text{on}\sqrt{3}\hat{i}+\hat{j}\\ & \sqrt{3}\text{and if}\alpha =2+\sqrt{3}\beta ,\text{then possible}\\ & \text{value(s) of}|\alpha |\text{is (are)}\end{array}& \text{(P) 1}\\ & \\ \begin{array}{cc}\text{(B)}& \text{Let}a\text{and}b\text{be real numbers such that}\\ & \text{the function}\\ & f\left(x\right)=\{\begin{array}{c}-3a{x}^2-2,x<1\\ bx+a^2,x\ge 1\end{array}\\ & \text{is differentiable for all}x\in R.\text{Then}\\ & \text{possible value(s) of}a\text{is (are)}\end{array}& \text{(Q) 2}\\ & \\ \begin{array}{cc}\text{(C)}& \text{Let}\omega \ne 1\text{be a complex cube root of}\\ & \text{unity. If}(3-3\omega +2{\omega }^2{)}^{4n+3}+\\ & (2+3\omega -3{\omega }^2{)}^{4n+3}+(-3+2\omega +3{\omega }^2{)}^{4n+3}=0,\\ & \text{then possible value(s) of}n\text{is (are)}\end{array}& \text{(R) 3}\\ & \\ \begin{array}{cc}\text{(D)}& \text{Let the harmonic mean of two positive real}\\ & \text{numbers}a\text{and}b\text{be}4.\text{If}q\text{is a positive real}\\ & \text{number such that}a,5,q,b\text{is an arithmetic}\\ & \text{progression, then the value(s) of}|q-a|\text{is (are)}\end{array}& \text{(S) 4}\\ & \\ & \text{(T) 5}\\ & \end{array}$$

Option $\text{(D)}$ matches with which of the elements of right hand column?

Four particles of equal mass M move along a circle of radius R under the action of their mutual gravitational
attraction. The speed of each particle is

A particle is placed at rest inside a hollow hemisphere of radius R. The coefficient of friction between the particle and the hemisphere is $\mu =\frac{1}{\sqrt{3}}$. the maximum height upto which the particle can remain stationary is

A real gas behaves as an ideal gas at

A 300 g mass has a velocity of $(3\hat{i}+4\hat{j})m/s$ at a certain instant. What is its kinetic energy

A rat of mass m falls from a height h onto the end of a platform, as shown in the figure. The spring is initially un-stretched and the mass of the platform can be neglected. Assuming that there is no loss of energy , themaximum elongation of the spring is

A section of an infinite rod of charge having linear charge density λ$\lambda$ which is constant for all points on the line.
Electric field E at a distance r from the line is

Find the period of the free oscillations of the arrangement shown below, if mass $M_1$ is pulled down a little.
[Force constant of the spring is $k$ and mass of the fixed pulley is negligible]

A spring of spring constant $240N{m}^{-1}$ is compressed by $10cm$ whereas another similar spring is extended by $10cm$. The difference of the stored potential energies of two springs is

A transverse wave of amplitude $0.5\text{mm}$ and frequency $100\text{Hz}$ is produced on a wire stretched to a tension of $100\text{N}$. If the wave speed is $100\text{m/s}$. What average power is the source transmitting to the wire?

The displacement of a particle executing simple harmonic motion is given by
$y=A_0+A\sin \omega t+B\cos \omega t$. Then, the amplitude of its oscillation is given by

A container is filled with liquid upto height $H$ as shown in figure. There are $2$ holes in the container such that water coming out from them have same range. If the range of water coming out of the holes is half of maximum range, then the distance $x$ between these holes is

A horizontal straight conductor of mass m and length l is placed in a uniform vertical magnetic field of magnitude B. An amount of charge Q passes through the rod in a very short time such that the conductor
begins to move only after all the charge has passed through it . Its initial velocity will be

A brass rod of length 2 m and cross-sectional area $2{\text{cm}}^2$ is attached end to end to a steel rod of length L and cross-sectional area $1{\text{cm}}^2$. The compound rod is subjected to equal and opposite pulls of magnitude $5\times {10}^4\text{N}$ at its ends. If the elongations of the two rods are equal, then the length (in m) the steel rod(L) is___

$[Y_B=1\times {10}^{11}\text{N}/{\text{m}}^2$ and $Y_S=2\times {10}^{11}\text{N}/{\text{m}}^2]$

Two equilateral triangles ABC and DEF have same centroid. The ratio of sides is 4 : 2. The resistance per unit length is constant. The resistance in AB is $10\Omega$ . The equivalent resistance between A and B is

For a particle executing S.H.M. the displacement $x$ is given by $x=A\cos \omega t$. Identify the graph which represents the variation of potential energy $\text{(P.E.)}$ as a function of time $t$ and displacement $x$.

Two bodies of different masses are dropped from heights of $2\text{m}$ respectively, then the ratio of the time taken by them is

If potential energy density is twice the average rate of transmission of potential energy. The speed of transverse wave is

In a rotor, a hollow vertical cylindrical structure rotates about its axis and a person rests against the inner wall. At a particular speed of the rotor, the floor below the person is removed and the person hangs resting against the wall without any floor. If the radius of the rotor is 2 m and the coefficient of static friction between the wall and the person is 0.2, find the minimum speed of rotor at which the floor may be removed. Take g = 10 m/$s^2$.

A missile of mass 1 kg is moving with speed 10 m/s along the +ve x direction. Its target is a car weighing 100 kg, moving with 1 m/s also in the +ve x direction. The missile hits the target but doesn't burst. Find the combined velocity of car-missile system?

Find the unit vector in the direction of the resultant of vectors $\hat{i}+2\hat{j}+3\hat{k},-\hat{i}+2\hat{j}+\hat{k}$ and $3\hat{i}+\hat{j}$.

The energy radiated by a black body at $2300\text{K}$ is found to have a maximum intensity at a wavelength $1260\text{nm}$, its emissive power being $8000{\text{W/m}}^2$. When the body is cooled to a temperature $T\text{K}$, the emissive power is found to decrease to $500{\text{W/m}}^2$. Find the temperature $T$.

A car is going at a speed of $6\text{m/s}$ when it encounters a $15\text{m}$ slope of angle ${30}^{\circ }$. The friction coefficient between the road and the tyre is $0.5$. The driver applies the brakes.
The minimum speed of the car with which it can reach the bottom is around $(g=10{\text{m/s}}^2)$

A Carnot engine works between temperatures ${127}^{\circ }\text{C}$ and $-{73}^{\circ }\text{C}$ . In process $1$, by increasing the temperature of source by ${50}^{\circ }\text{C}$, efficiency of engine becomes ${\eta }_1$. In process $2$, by decreasing the temperature of sink by ${50}^{\circ }\text{C}$, efficiency of engine becomes ${\eta }_2$. Then which of the following option is correct?

In the manometer as shown, $2$ immiscible fluids - mercury $(\rho =13600{\text{kg/m}}^3)$ and water $(\rho =1000{\text{kg/m}}^3)$ are used as manometric fluids. The water end is exposed to the atmosphere $\left(100\text{kPa}\right)$ and the mercury end is exposed to a gas. At this position, the interface between the fluids is at the bottom most point of the manometer. The value of $h$ is found to be $9.45\text{m}$. The height of the mercury column is given to be $75\text{cm}$. Find the gauge pressure of the gas. $(g=9.8{\text{m/s}}^2)$

Two metallic spheres of radii $1cm$ and $3cm$ are given charges of $-1\times {10}^{-2}C$ and $5\times {10}^{-2}C$ respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

The four quantum number of the outermost electron of K (At. No. = 19) are:

Why why angle of incedence is equal to angle of reflection .

Two discs of radii 4 cm and 2 cm respectively are attached as shown in the figure. The new centre of mass of the system from '$C_1$' is

Two spheres made of same material have radii r and 2r. They are initially touching each other and start moving out along the line joining their centres with velocities 4v and v respectively. The velocity of their centre of mass is

Find the MOI of the uniform rod about the given axis

A wire of mass $M$ and length $L$ is bent in form of a square. Calculate the MI of the square about the central axis perpendicular to the plane.

A ball of mass $1\text{kg}$ moves inside a smooth fixed spherical shell of radius $1\text{m}$ with an initial velocity $v=5\text{m/s}$ from the bottom. What is the total force acting on the particle at point $B$?

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction $x_1\left(t\right)=Asin\omega t$ and $x_2\left(t\right)=Asin(\omega t+\frac{2\pi }{3})$. Adding a third sinusoidal displacement $x_3\left(t\right)=Bsin(\omega t+\varphi )$ brings the mass to a complete rest. The values of B and $\varphi$ are

In a liquid with density $1300\frac{kg}{m^3}$, longitudinal waves with frequency 400 Hz are found to have wavelength 8.00 m. Calculate the bulk modulus of the liquid.