Explore topic-wise InterviewSolutions in Current Affairs.

A particle of mass $M$ at rest decays into two particles of masses $m_1$ and $m_2$, having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles, ${\lambda }_1/{\lambda }_2$ is

An ant fell in a hemispherical bowl of radius 'r'. Now the ant is trying to climb out of it. Find the maximum height that the ant can reach above the bottom most point of the bowl. Given the coefficient of static friction between ant and bowl is '$\mu$' and the ant climbs very slowly.

The van der Waals constants for $HCl$ are $a=371.843{\text{kPadm}}^6{\text{mol}}^{–2}$ and $b=40.8{\text{cm}}^3{\text{mol}}^{-1}$ .What is the critical pressure of $HCl$ ?

A block of mass m moving with speed v compresses a spring through distance x before its speed is halved. The value of spring constant is

A cantilever beam of span 'L' is subjected to a downward load of 800 kN uniformly distributed over its length and a concentrated upward load P at its free end. For vertical diplacement to be zero at the free end,the value of P is :

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In an experiment on photoelectric effect, light of wavelength $400\text{nm}$ is incident on a caesium plate at the rate of $5.0\text{W}$. The potential of the collector plate is made sufficiently positive with respect to the emitter so that the current reaches its saturation value. Assuming that on the average, one out of every ${10}^6$ photons is able to eject a photoelectron, find the photocurrent in the circuit.

[Use $hc=1240\text{eV (nm)}$]

A
4.5 cm needle is placed 12 cm away from a convex mirror of focal
length 15 cm. Give the location of the image and the magnification.
Describe what happens as the needle is moved farther from the mirror.

A stationary $P{b}^{200}$ nucleus emits an alpha-particle with kinetic energy $K_{\alpha }$. The fraction of recoil energy of the daughter nucleus to the total energy liberated is :

The magnetic flux through a coil varies with time as $\varphi =5t^2+6t+9$. The ratio of $emf$ at $t=3\text{s}$ to $t=0\text{s}$ will be

A ring of external and internal radii $r_1$ and $r_2$ just touches the horizontal surface of a liquid of surface tension $\sigma$. The force required to pull the ring away from the surface is

In a heating experiment, it was noted that the temperature of liquid in a beaker rose at $4.0\text{K}$ per minute just before it began to boil, and $40$ minutes later, all the liquid had boiled away.

For this liquid, what is the value of ratio

$\frac{\text{specific heat capacity}}{\text{specific latent heat of vapourisation}}$ (in SI units)?

A charge $Q$ is placed at the centre of a imaginary hemispherical surface. Using symmetry arguments and Gauss's law, find the flux of the electric field due to this charge through the curved surface of the hemisphere as shown in the figure.

Moment of inertia $I$ of a solid sphere about an axis parallel to a diameter and at a distance $x$ from its centre of mass varies as

A ball is held at rest in position $A$ by two light cords. The horizontal cord is now cut and the ball swings to position $B$. What is the ratio of the tension in the cord at position $B$ to that at position $A$ originally?

In a children's park a heavy rod is pivoted at the centre and is made to rotate about the pivot so that the rod always remains horizontal. Two kids hold the rod near the ends and thus rotate with the rod as shown in figure. Let the mass of each kid be $15\text{kg}$, the distance between the points of the rod where the two kids hold it be $3.0\text{m}$ and suppose that the rod rotates at the rate of $20$ revolutions per minute. Find the force of friction exerted by the rod on one of the kids.

A force $\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$ where $k$ is a positive constant acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point $(a,0)$ and then parallel to the y-axis to the point $(a,a)$. The total work done by the force $\overrightarrow{F}$ on the particle is

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A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is :

The standard molar enthalpies of formation of cyclohexane (l) and benzene (l) at ${25}^{\circ }C$ are -156 and +49 kJ/mol. The standard enthalpy of hydrogenation of cyclohexene (l) at ${25}^{\circ }C$ is -119 kJ/mol. Estimate the magnitude of resonance energy.

A capacitor is connected to a $12\text{V}$ battery through a resistance of $10\Omega$. It is found that the potential difference across the capacitor rises to $4.0\text{V}$ in $1\mu \text{s}$. Find the capacitance of the capacitor. $(\ln \frac{3}{2}=0.405)$

A particle undergoing simple harmonic motion has time dependent displacement given by $x\left(t\right)=A\sin \frac{\pi t}{90}.$ The ratio of kinetic to potential energy of this particle at $t=210\text{s}$ will be:

An inductor coil stores $32\text{J}$ of magnetic field energy and dissipates energy as heat at the rate of $320\text{W}$ when a current of $4\text{A}$ is passed through it. Find the time constant of the circuit when this coil is joined across an ideal battery.

A sound wave of frequency $245\text{Hz}$ travels with the speed of $300{\text{ms}}^{-1}$ along the positive $x-\text{axis}$. Each point of the medium moves to and fro through a total distance of $6\text{cm}$. What will be the mathematical expression of the travelling wave?

A uniform rod of mass $M$ and length $L$ is hanging from point $P$ as shown in the figure. Find the elongation in its length due to the self weight of the rod. The Young's modulus of elasticity of the rod is $Y$ and cross-sectional area of the rod is $A$.

A body of mass $m$ thrown horizontally with velocity $v$, from the top of a tower of height $h$ touches the level ground at a distance of $250\text{m}$ from the foot of the tower. A body of mass $2m$ thrown horizontally with velocity $\frac{v}{2}$, from the top of a tower of height $4h$ will touch the level ground at a distance $x$ from the foot of tower. The value of $x$ is

Due to a point isotropic sonic source, loudness at a point is L = 60 dB. If density of air is $\rho =\left(\frac{15}{11}\right)kg/m^3$ and velocity of sound in air is v = 330 m/s, the pressure oscillation amplitude at the point of observation is $[I_0={10}^{-12}W/m^2]$

${}^{131}I$ is an isotope of Iodine that $\beta -$ decays to an isotope of Xenon with a half-life of $8\text{days}$. A small amount of a serum labelled with ${}^{131}I$ is injected into the blood of a person. The activity of the amount of ${}^{131}I$ injected was $2.4\times {10}^5\text{Becquerel (Bq)}$. It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After $11.5\text{hours},2.5\text{ml}$ of blood is drawn from the person's body, and gives an activity of $115\text{Bq}$. The total volume of blood in the person's body, in $\text{liters}$ is approximately _______.

The Young's modulus of the material of a wire is $6\times {10}^{12}N/m^2$ and there is no transverse(lateral) strain in it, then its modulus of rigidity will be