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When a beam of light of wavelength $\lambda$ is incident on the surface of a liquid at an angle $\theta$, the reflected ray is completely polarized. The wavelength of light in the liquid medium is

Three particles starts from origin at tha same time . One along positive x-axis with velocity v₁ second along positive y axis with velocity v₂ and third along the line y=x in such a speed that all three particles will always remain in a straight line , what is the velocity of third particle.

A thin hollow sphere of mass m is completely filled with an ideal liquid of mass m. When the sphere rolls with a velocity v kinetic energy of the system is equal to

A capacitor is charged to a certain potential difference and stores some energy. In order to double the energy stored in the capacitor, the potential difference must be increased nearly by

A
long solenoid with 15 turns per cm has a small loop of area 2.0 cm²
placed inside the solenoid normal
to its axis. If the current carried by the solenoid changes steadily
from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop
while the current is changing?

Light of two different frequencies whose photons have energies 1 eV and 2.5 eV respectively, successively illuminate a metallic surface whose work function is 0.5 eV. Ratio of maximum speeds of emitted electrons will be

A capacitor is charged to $10\mu C$ and is at potential 5V. This capacitor is now isolated from any circuit. Now a dielectric of dielectric constant k=3 is placed between the plates such that there is no empty space left between the plates. What is the change in energy of the capacitor?

If we shift a body in equilibrium from A to C in a gravitational field via path AC or ABC by a force F. Then

If $y=\frac{\ln x}{x}$, then $\frac{dy}{dx}$ will be

A solid sphere is kept on a rough horizontal surface. A horizontal force ${}^{\prime }{F}^{\prime }$ is applied at centre. Calculate the acceleration of the sphere.

What is the total strain energy of a member subjected to an axial stress f(E = Young's modulus)?

Find the maximum magnifying power of a compound microscope having a $25\text{D}$ lens as the objective, a $5\text{D}$ lens as the eyepiece and a separation of $30\text{cm}$ between the two lenses. The least distance for clear vision is $25\text{cm}$.

A brick of mass 2 kg begins to slide down on a plane inclined at an angle of ${45}^o$ with the horizontal. The force of friction will be

A person $P$ is $600\text{m}$ away from the station when train is approaching station with $72\text{km/h}$, it blows a whistle of frequency $800\text{Hz}$ when $800\text{m}$ away from the station. Find the frequency heard by the person. Speed of sound $=340{\text{ms}}^{-1}$.

A steel wire is $1\text{m}$ long and $1{\text{mm}}^2$ in area of cross section. If it takes $200\text{N}$ to stretch this wire by $1\text{mm}$. How much force will be required to stretch a wire of same material as well as same cross-section area from its normal length of $2\text{m}$ by a length of $20\text{mm}$?

A positive point charge +Q is fixed in space. A negative point charge -q of mass m revolves around a fixed charge in elliptical orbit. The fixed charge +Q is at one focus of the ellipse. The only force acting on negative charge is the electrostatic force due to positive charge. Then which of the following satement is true.

Figure shows two blocks in contact sliding down an inclined surface of inclination ${30}^{\circ }$. The friction coefficient between the block of mass $2.0kg$ and the incline is ${\mu }_2$, and that between the block of mass $4.0kg$ and the incline is ${\mu }_1$. Calculate the acceleration of the $2.0kg$ block if ${\mu }_1=0.30$ and ${\mu }_2=0.20$. Take $g=10m/s^2$.

For the following circuits, the potential difference between X and Y in volt is

A block of mass $5\text{kg}$ slides down on a rough inclined plane of coefficient of friction $0.75$ having angle of inclination ${37}^{\circ }$ as shown in the figure. Initially if the block is at rest on the top of inclined plane of length $2\text{m}$, then the work done against the friction in moving the block to the bottom of inclined plane is (Take $g=10{\text{m/s}}^2$).

A body of mass 'm' collides against a wall with a velocity 'v' and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive)

The charge supplied by the battery in the circuit shown in the figure is-

A heavy homogenous cylinder has mass m and radius R. It is accelerated by a force F which is applied to the cylinder. The coefficient of static friction is sufficient for the cylinder to roll without slipping then

Evaluate: ${\int }_2^5\text{(ln x)dx}$

The kineti energy of a charged particle decreases by 10 J as it moves from a point at potential 100 V to a point at potential 200 V. Find the charge on the particle.

A child weighing 30 kg slides down a rope hanging from the branch of a tall tree. If the force of friction acting against him is 2 N, what is the acceleration of the child (Take g = 10m / s.)

In the following figure an isolated charged conductor is shown. The correct statement will be: -

A car start from rest and acquire a velocity of $54\text{km/h}$ in $2\text{sec}$. Find the acceleration of the car.

A body moves over one-fourth of a circular arc in a circle of radius $r$. The magnitude of distance travelled and displacement will be respectively

A hydraulic automobile lift is designed to lift cars with a maximum mass of $300\text{kg}$. The area of cross-section of the piston carrying the load is $500{\text{cm}}^2$. What maximum pressure would smaller piston have to bear?

When a 13.2 kg mass is placed on top of a vertical spring, the spring compresses by 5.93 cm. Find the force constant of the spring.