Explore topic-wise InterviewSolutions in .

The time period of a spring-mass system is $T$ in air. When the mass is partially immersed in water, the time period of oscillation is $T^{\prime }$. Then:





[Assume the mass is cubical]

Two identical billiard balls are in contact on a smooth table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is

Derivative of $f\left(x\right)=\frac{e^x}{\cos \left(x^2\right)}$ is

Two bodies, a sphere and a cube made of the same material and having the same volume are heated to the same temperature and allowed to cool in the same surroundings. The ratio of the amount of radiation emitted in equal time intervals will be

The specific heat of a metal at low temperatures varies according to $S=a{T}^3$ where $a$ is a constant and $T$ is absolute temperature. The heat energy needed to raise the temperature of unit mass of the metal from $T=1K$ to $T=2K$ is

The surface tension of soap solution is $T=0.03{\text{Nm}}^{-1}$. If the size of a soap bubble is increased from a radius of $3\text{cm}$ to $5\text{cm}$, the work done in increasing the size of the soap bubble is

If the earth is at one-fourth of its present distance from the sun, the duration of the year will be

In previous question after what time the passenger catches bus ?

A spherical ball of radius $1\text{cm}$ coated with a metal having emissivity $e=0.3$ is maintained at $1000\text{K}$ temperature and suspended in a vaccum chamber whose walls are maintained at $300\text{K}$. Find the rate at which electrical energy is to be supplied to the ball to keep its temperature constant. $[\sigma =5.67\times {10}^{-8}\text{W}{\text{m}}^{-2}{\text{K}}^{-4}]$

If the momentum of a body is increased n times, its kinetic energy increases

If a body A of mass M is thrown with velocity V at an angle of ${30}^{\circ }$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of ${60}^{\circ }$ to the horizontal. The ratio of horizontal range of A to B will be

Which of the following can be a valid distance time graph?

In the figure shown, a point object $O$ is placed in air. A spherical boundary of radius of curvature $1.0m$ separates two media. $AB$ is the principal axis. The refractive index above $AB$ is $1.6$ and below $AB$ is $\mathrm{2.0.}$ The separation between the images formed due to refraction at the spherical surface is

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its center. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ${\omega }_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega$(t) will vary with time t as

Graph of V vs I is given in figure. Its ln(P) vs ln(I) graph will be

A marble block of mass $2\text{kg}$ lying on ice when given a velocity of $6\text{m/s}$ is stopped by friction in $10\text{s}$. Then the coefficient of friction is

A monochromatic light source of intensity 5 mW emits $8\times {10}^{15}$ photons per second. This light ejects photoelectrons from a metal surface. The stopping potential for this setup is 2.0 V. Calculate the work function of the metal.

A tuning fork gives 4 beats with 50 cm length of a sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is

The image of an object placed on the principal axis of a concave mirror of focal length 12 cm is formed at a point which is 10 cm more distance from the mirror than the object. The magnification of the image is

An automobile moves on a rough road with a speed of $54{\text{kmh}}^{-1}$. The radius of its wheels is $0.45\text{m}$ and the moment of inertia of the wheel about its axis of rotation is $3{\text{kg.m}}^2$. If the wheel is brought to rest in $15\text{s}$, then find magnitude of average torque transmitted by the brakes to wheel. Assume no slipping at all points of contact.

A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half-life period of element will be

A particle moves under the effect of a force F = Cx from x = 0 to $x=x_1$ . The work done in the process is

A ray incident at an angle ${53}^{\circ }$ on a prism and emerges at an angle of ${37}^{\circ }$ as shown in figure. If the angle of incidence is made ${50}^{\circ }$ then possible value of the angle of emergence is

A semi circular ring of radius $2\pi$ is situated in $X-Y$ plane having centre at $(10,10)$ as shown in the figure below. Find the co-ordinates of centre of mass of the ring.

A swimmer jumps upwards from a diving board( A) and while she is going up another swimmer just walks off the diving board(B). Then throughout time of flight swimmer B will see swimmer A

A particle is placed at the origin and a force $F=kx$ is acting on it (where, $k$ is a positive constant). If $U\left(0\right)=0$, the graph of $U\left(x\right)$ versus $x$ will be (where $U$ is the potential energy function)

One end of steel wire is fixed to ceiling of an elevator moving up with an acceleration of $2{\text{m/s}}^2$ and a load of $10\text{kg}$ hangs from the other end. Area of cross - section of the wire is $2{\text{cm}}^2$. The longitudinal strain in the wire is

$[Y=2\times {10}^{11}{\text{N/m}}^2]$

A particle starts from rest, travelling on a circle with constant tangential acceleration. The angle between velocity vector and acceleration vector, at the moment when the particle completes half the circular track is

A hockey player receives a corner shot at a speed of $15\text{m/s}$ at angle ${30}^{\circ }$ with y - axis and then shoots the ball along x - axis with the speed $30\text{m/s}$. If the mass of the ball is $150\text{grams}$ and it remains in contact with the hockey stick for $0.01\text{s}$, the force exerted on the ball along x - axis is

Dimentional formula of permeability of free space ${\mu }_0$ is given by

Suppose that the electromagnetic wave in vacuum is

$\overrightarrow{E}=\{\left(3.1\frac{N}{C}\right)\cos \left[(1.8\frac{rad}{m}\right)y+(5.4\times {10}^6\frac{rad}{s})t]\hat{i}$

What is the frequency?

A man is approaching a plane mirror with constant acceleration of 4 $m/s^2$. Initially the person is at rest. Mirror is moving towards the person with a constant velocity of 4 m/s. The correct variation of velocity of image of man (wrt ground) vs time is best given by consider leftwards as positive)

A vector has component along the $x$-axis equal to $25\text{unit}$ and along the $y$-axis equal to $60\text{unit}$. Then the position vector will be

A small spherical steel ball is placed a little away from the centre of a large concave mirror of radius of curvature R = 2.5 m. The ball is then released. What is the time period of the motion? Neglect friction and take g = $10m{s}^{-2}$

A liquid of density $\rho$ and surface tension $\sigma$ rises to a height $h$ in a capillary tube of diameter $d$. The potential energy of the liquid in the capillary tube is:

[Assume liquid to be perfectly wetting in nature]

A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=kt$ ($k$ is a constant) acts along the direction of motion of particle for the time interval $T$ so that its momentum changes from $p$ to $5p$. The value of $T$ is

A constant force $\overrightarrow{F_1}=(2\hat{i}-4\hat{j})\text{N}$ displaces a particle from $(1,-1,2)$ to $(-1,-1,3)$ and then another force $\overrightarrow{F_2}=(3\hat{i}+4\hat{j})\text{N}$ displaces it from $(-1,-1,3)$ to $(5,5,5)$ (displacement being measured in metres). Find the total work done.

The initial conditions of a particle executing SHM are as shown in the figure. Find the phase constant $\varphi$ of the particle.

Given: Range of $\varphi$ is $[0,2\pi ]$

A solid sphere of radius $R$ is surrounded by a liquid in a cylindrical container. A massless piston of area $A$ floats on the surface of the liquid. Find the value of bulk modulus, if the fractional decrease in the radius of the sphere is $\kappa$ when a mass $M$ is placed on the piston to compress the liquid. [Neglect the pressure variation between the piston and sphere and consider $\kappa$ as positive]

The spring balance A reads 2kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation:

The control rod in a nuclear reactor is made of

Find the magnetic induction at the origin in the figure shown

A particle with a charge 2μC is hanging in air above a similarly charged conducting surface whose surface charge density is $43.3\times {10}^{-12}C/m^2$. The mass of particle is

Eight equal drops of water are falling through air with a steady velocity of $5\text{cm/sec}$. If smaller drops combine to form a single large drop, then the terminal velocity (in $\text{cm/sec}$) of this large drop is

A long conveyor belt is designed to transport packages of various weights. Each $20kg$ package has a coefficient of kinetic friction $0.25$. If the speed of the conveyor belt is $10m/s$ and then it suddenly stops, the distance the package will slide before coming to rest is