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In the circuit shown in figure, Find energy stored in $4\mu \text{F}$ capacitor at the steady state.

The nuclear charge $\left(Ze\right)$ is non-uniformly distributed within a nucleus of radius $R$. The charge density $\rho \left(r\right)$( charge per unit volume) is dependent only on the radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. The electric field within the nucleus is generally observed to be linearly dependent on $r$. This implies

In a region of space, suppose there exists a uniform electric field E= 10i (V/m) If a positive charge moves with a velocity v=-2j, its potential energy at this moment.

(1) Increases

(2) Decreases

(3) Does not change

(4) Both (1) and (2)

If two thin lenses of focal length f₁ and f₂ are held in contact then the focal length of the combination will be

A particle of mass $m$ attached to a string of length $l$ fixed at a point such that it can perform circular motion in a vertical plane. The particle is imparted a velocity of $\sqrt{8gl}$ at the lowest position by a sharp hit. Find the ratio of tension in string at the lowermost position to the tension in the string at the topmost position of the vertical circular path. Take $g=10{\text{m/s}}^2$.

A free atom of iron emits $K_{\alpha }\text{X}$-rays of energy $6.4\text{keV}.$ Calculate the recoil kinetic energy of the atom.

Mass of an iron atom $=9.3\times {10}^{-26}\text{kg}.$

1. 1550

If position of $B$ with respect to $P$, is $+2\text{m}$ and position of $C$ with respect to $P$ is $-4\text{m}$. Where $B,P,C$ are the points along $X-$axis, then what will be the position of $B$ with respect to $C$ ?

In
a Van de Graaff type generator a spherical metal shell is to be a 15
× 10⁶
V electrode. The dielectric strength of the gas surrounding the
electrode is 5 × 10⁷
Vm⁻¹.
What is the minimum radius of the spherical shell required? (You will
learn from this exercise why one cannot build an electrostatic
generator using a very small shell which requires a small charge to
acquire a high potential.)

If the error in the measurement of mass of a body be 3% and in the measurement of velocity be 2%. What will be the maximum possible error in calculation of kinetic energy

If $V$ is the gravitational potential on the surface of the earth, then what is its value at the centre of the earth?

(Assume that mass distribution is uniform)

Find out the electric force experienced by $+1\mu \text{C}$ charge at point $\text{A}(0,1,2)\text{m}$ due to a point charge $-20\mu \text{C}$ situated at point $\text{B}(\sqrt{2},0,1)\text{m}$.

A person can see clearly objects only when they lie between $50\text{cm}$ and $250\text{cm}$ respectively. The person uses a lens of power $2\text{D}$ , while reading at $25\text{cm}$. With this lens, find the maximum distance clearly visible for the person?

Find the value of $\frac{\tan {\theta }_1}{\tan {\theta }_2}$





Where,

$V_s\Rightarrow \text{stopping potential}\left(\text{V}\right)$

$f\Rightarrow \text{frequency of radiation}\left({\text{s}}^{-1}\right)$

$K{E}_{max}\Rightarrow \text{maximum kinetic energy}\left(\text{J}\right)$.

Find the integral of the function $\frac{1}{x^2+6x+5}$

Air is pushed into a soap bubble of radius 'r' to double its radius. If the surface tension of the soap solution is S, the work done in the process is?

Two particles having masses $3\text{kg}$ and $6\text{kg}$ are situated in a plane perpendicular to line $AB$ at a perpendicular distance of $2\text{m}$ and $4\text{m}$ respectively as shown in figure. Find the moment of inertia about an axis $A^{\prime }{B}^{\prime }$ parallel to $AB$.

The op-amp circuit in the figure given below is ideal



The current $I_L$ throug the load resistor $R_L$ is

The figure shows arrangements of springs. They have stiffness $k_1$ and $k_2$ as marked. Which of the following arrangements offers a stifness = $\frac{2k_1{k}_2}{k_1+2k_2}?$

Two rods of length $L_2$ and coefficient of linear expansion ${\alpha }_2$ are connected freely to a third rod of length $L_1$ of coefficient of linear expansion ${\alpha }_1$ to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of $L_1$ which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of -5.00$\hat{i}$​ m/s and an acceleration of + 12.5$\hat{j}$​ m/s². What are the x and y coordinates of the center of the circular path?

You are given two converging lenses of focal lengths, $1.25\text{cm}$ and $5\text{cm}$ to design a compound microscope. It is desired to have a magnification of $30$ in case of normal adjustment. Find out the separation between the objective lens and the eyepiece.

A helicopter rises from rest on the ground vertically upwards with a constant acceleration $g$. A food packet is dropped from the helicopter when it is at a height $h$. The time taken by the packet to reach the ground is close to



[$g$ is the acceleration due to gravity]

If one mole of an ideal gas at $(P_1,V_1,T)$ is allowed to expand reversibly and isothermally $(A$ to$B)$ its pressure is reduced to $\frac{1}{2}$ of original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of initial value $(B\to C)$. Then it is restored to its initial state by a reversible adiabatic compression $(C$ to $A)$. The net work done by the gas is equal to :

The displacement of a particle executing simple harmonic motion is given by

$x\left(t\right)=2\sin \left(2\pi t\right)+2\cos (2\pi t+\frac{\pi }{6})$

The total energy of the particle is $(m=1\text{kg}$)

What is the representative geometric mean size of an aggregate sample if its fineness modulus is 3.0?

newtonians mechanics

In the feedback scheme shown in figure, the time-constant of the closed loop system will be

How does the mutual inductance of a pair of coils change when distance between the coils is increased?

If the time of flight of a bullet over a horizontal range $R$ is $T$, then inclination of the direction of projection with the horizontal is