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Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${\omega }_1$ and ${\omega }_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss in coinciding of energy during this process is

In the quadratic equation, $pq{x}^2-(p^2+q^2)x+pq=0,$ then find values of $x$.

A disc of moment of inertia $\frac{9.8}{{\pi }^2}{\text{kg m}}^2$ is rotating at $600\text{rpm}$. If the frequency of rotation changes from $600\text{rpm}$ to $300\text{rpm}$, then what is the work done approximately?

A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths ${\lambda }_A$ to ${\lambda }_B$ after the collision is

A uniformly charged rod of length $4\text{cm}$ and linear charge density $\lambda =30\mu \text{C/m}$ is placed as shown in figure. Calculate the $x-$component of electric field at point $\text{P}$.

As shown in figure, a metal rod makes contact with a partial circuit and completes the circuit. The circuit area is perpendicular to a magnetic field with B = 0.15 T. If the resistance of the total circuit is $3\Omega$ , the force needed to move the rod as indicated with a constant speed of $2m{s}^{-1}$ will be equal to

A plane loop shown in the figure is shaped in the form of two squares with sides $a\text{and}b$ is introduced into a uniform magnetic field at right angles, to the loop's plane. The magnetic induction varies with time as $B=B_0\sin \omega t$. Find the amplitude of the current induced in the loop if its resistance per unit length is equal to $r$. The induction of the loop is negligible.

A car is moving in a circular horizontal track with a constant speed. The centripetal force acting on the car is $75\text{N}$ . If the car’s speed is doubled, what is the new centripetal force required for the car to drive on the same circular track?

A small
candle, 2.5 cm in size is placed at 27 cm in front of a concave
mirror of radius of curvature 36 cm. At what distance from the mirror
should a screen be placed in order to obtain a sharp image? Describe
the nature and size of the image. If the candle is moved closer to
the mirror, how would the screen have to be moved?

A solid cylinder of radius R & length 3R is made of a material having density $\rho$. Now two hemispheres each of radius R is removed from two ends of cylinder as shown in figure. Determine the moment of inertia of this object about axis of cylinder

When ${\text{U}}^{238}$ nucleus originally at rest, decays by emitting an alpha particle having a speed $u$, the recoil speed of the residual nucleus is

A man can row a boat with a speed of $4\frac{km}{hr}$ in still water. If he is crossing a river where the current is $2\frac{km}{hr},$ and the width of the river is 12 km, the time taken by him to cross with zero drift is

If $\overrightarrow{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3}\hat{k}$, then find the Electric flux through surface of area $100{\text{m}}^2$ lying in the $\text{xy-plane}$ (in $\text{Vm}$)

A magnet of magnetic moment $M$ and length $2l$ is bent at its mid point such that the angle of bending is ${60}^{\circ }$. The new magnet moment is-

1. 10

A ball is bouncing down a set of stairs. The coefficient of restitution is $e$. The height of each step is $d$ and the ball bounces one step at each bounce. After each bounce the ball rebounds to a height $h$ above the next lower step. Neglect height of each step in comparison to $h$ and assume the impacts to be effectively head on. Which of the following relation is correct? (given that $h>d$)

The length of perpendicular $\left(\text{in units}\right)$ drawn from the point $⟨-3,-\frac{5}{2},1⟩$ to the line $\overrightarrow{r}=(11\hat{i}-2\hat{j}-8\hat{k})+\lambda (10\hat{i}-4\hat{j}-11\hat{k})$ is:

A point charge Q is placed at one of the edge of a cube as shown. Total electric flux passing through this cube is



एक बिन्दु आवेश Q को दर्शाए अनुसार एक घन की किसी एक भुजा पर रखा गया है। इस घन से गुजरने वाला कुल विद्युत फ्लक्स है

Two protons of masses $1.6\times {10}^{-27}\text{kg}$, goes round in a concentric circular orbits of radii $0.50\text{nm}$ and $1\text{nm}$ experience centripetal forces in the ratio of $1:4$, then the ratio of frequency of revolution of the protons is (Assume no force of interaction between protons )

In which case, the nature of the image will be virtual, erect and enlarged ?

Time constant of a capacitor and capacitance are 5s and $100nF$. It is charged from zero by a cell of emf$10V$ through a resistor. The charge on it after 3 s is.

A ball is projected upwards from the top of a tower with a velocity of $50{\text{ms}}^{-1}$ making an angle of ${60}^{\circ }$ with the vertical. If the height of the tower is $70\text{m}$, then the ball will hit the ground in

In a resonance column experiment, a tuning fork of frequency $850\text{Hz}$ is used. The first resonance is observed when the air column has a length of $9\text{cm}$ and the second resonance is observed when the air column has a length of $29\text{cm}$. The pressure node is formed at distance $X$ above the open end. Then, value of $X$ is

A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in $m/s^2$ is

The gravitational field due to a mass distribution is $E=\frac{K}{x^3}$ in the x - direction (K is a constant).Taking the gravitational potential to be zero at infinity, its value at a distance x is:

The resistance of hot tungsten filament is about 10 times to that of cold tungsten filament. What will be the resistance of 100 W and 220 V lamp when not in use?

1. 1.5

Find the dimensions of a/b in the equation:

P= (a-t^{​​​​2})/bx

Where

P is pressure, x is distance and t is time.

In the movie gravity, astronauts Sandra Bullock & George Clooney are stranded in space and connected by a string. To come closer to each other they both start pulling the string from their ends. Assuming that if the astronauts are pulling the string with a force F then the tension in the string should be equal and in opposite direction and should pull the astronaut (According to Newton's 3rd law).

Then in that case the net force on each astronaut should be 0 and they shouldn't move according to 1st law. Why are the moving towards each other?

A force $\overrightarrow{F}=(5\hat{i}+3\hat{j}+2\hat{k})\text{N}$ is applied over a particle which displaces it from origin to the point $\overrightarrow{r}=(2\hat{i}-\hat{j})\text{m}$. The work done on the particle is

A wire of mass $m$ and length $l$ can slide freely on a pair of smooth, vertical rails as shown in the figure. A magnetic field $B$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance $C$. Find the acceleration of the wire, neglecting any electric resistance.

A uniform metal chain is placed on a rough table such that one end of chain hangs down over the edge of the table. When one-third of its length hangs down over the edge, the chain starts sliding. Then, the value of coefficient of static friction is-

A charge $Q$ is placed at a distance $L$ from the charge $-2q$ as shown in figure.



The system of three charges will be in equilibrium, if $Q$ is equal to