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In an interference experiment, third bright fringe is obtained at a point on the screen with a light of $700\text{nm}$. What should be the wavelength of the light in order to obtain $5^{th}$ bright fringe at the same point?

A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.

The figure shows two blocks of masses $6\text{kg}$ and $4\text{kg}$ placed on a frictionless surface and connected with spring. An external kick gives a velocity $15\text{m/s}$ to $6\text{kg}$ block and $10\text{m/s}$ to $4\text{kg}$ block in the opposite direction as shown. Find the velocity gain by the centre of mass of the system.

A force $F=(2x+3x^2)\text{N}$ acts on a particle in $x-$ direction, where $F$ is in Newton and $x$ is in metre. Find the work done by this force for the displacement from $x=0\text{m}$ to $x=3\text{m}$.

what is difference betqeen physical quantity and dimension? qith examples

If $|\overrightarrow{A}+\overrightarrow{B}|$ =$|\overrightarrow{A}-\overrightarrow{B}|$ then the angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is

A particle is thrown upwards such that its maximum height is $4h$. The height of the particle where speed is $3/4^{th}$ of the maximum speed is

A block of mass 250 g is kept on a vertical spring of spring constant 100 N/m fixed from below. The spring ' is a now compressed to have a length 10 cm shorter than . its natural length and the system is released from this position. how does the block rise ? Take $g=10m/s^2$

For every action, there is an equal and opposite reaction. Do the bodies exerting action and reaction have to be in contact?

In the figure shown, both the blocks are of equal mass of $10kg$ and $F=300N$. Find the value of tension $T$ in the string in between the blocks.

A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface

If $\overrightarrow{A}=4\hat{i}-3\hat{j}$ and $\overrightarrow{B}=6\hat{i}+8\hat{j}$ then magnitude and direction of $\overrightarrow{A}+\overrightarrow{B}$ will be

Two small balls A and B, each of mass m, are joined rigidly by a light horizontal rod of length L. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed $\omega$ about the axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. Find the new angular speed of the rod.

Minimum thickness of a mica sheet (which should be placed in front of one of the slits in YDSE) required to reduce the intensity at the centre of screen to half of maximum intensity is (the refractive index of the sheet is $3/2$) Assume that the sheet does not absorb any light

In the given circuit, the potential drop across the capacitor must be

A boy pulls a toy having two carriages placed on a frictionless table by applying a force of 1.5 N at 30 degrees in a vertical plane . Calculate the acceleration of the 40g carriage . The acceleration of the 20g carriage and the tension in the string attached between the 2 carriages .

Find the decrease in the volume of a sample of water from the following data. Initial volume $=1000c{m}^3,$ initial pressure $={10}^{5}N{m}^{-2}$ final pressure $={10}^{6}N{m}^{-2},$ compressibility of water $=50\times {10}^{-11}{m}^2{N}^{-1},$

The current $I$ drawn from the $5\text{Volt}$ source will be

I have a container that is 20cm tall and filled fully with water. The lift accelerates up at 10 $\text{m}/{\text{s}}^2$. What is the pressure difference between the top surface of the water and the bottom of the container(in pascal)? Take density of water as 1kg/lit.

A splitting tensile test is performed on cylinder of diameter D and length L. If the ultimate load is P, then splitting tensile strength of concrete is given by

A stone is thrown vertically upwards with an initial velocity of $30\text{m/s}$. The time taken for the stone to rise to its maximum height is
[Take $g=10{\text{m/s}}^2$]

Two cells of e.m.f $E_1$ and $E_2(E_1>E_2)$ are connected as shown in figure. When a potentiometer is connected between $\text{A}$ and $\text{B}$, the balancing length of the potentiometer wire is $300\text{cm}$. On connecting the same potentiometer between $\text{A}$ and $\text{C}$, the balancing length is $100\text{cm}$. The ratio $E_1/E_2$ is

Phase angle between voltage and current in RLC circuit is given by

In column I, a uniform bar of uniform cross-sectional area under the application of forces is shown in the figure and in Column II, some effects/phenomena are given. Match the entries of Column I with the entries of Column II.

. (take $g=10{\text{ms}}^{-2}$)

Which of these is a unit vector that makes an angle of ${60}^{\circ }$ with the positive direction of x axis ?