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A neutron moving at a speed v undergoes a head-on elastic collision with a nucleus of mass number A at rest. The ratio of the kinetic energies of the neutron after and before collision is

A sphere of radius $R$ is in contact with a wedge. The point of contact is $\frac{R}{5}$ from the ground as shown in the figure. Wedge is moving with velocity $20m{s}^{-1}$ towards left. The velocity of the sphere at this instant will be

A train approaching a platform at a speed of 54 km/h sounds a whistle. An observer on the platform finds its frequency to be 1620 Hz. The train passes the platform keeping the whistle on and without slowing down. What frequency will the observer hear after the train has crossed the platform? The speed of sound in air = 332 m/s.

A parallel plate capacitor is made by stacking n equally spaced plates connected alternately. If the capacitance between any two plates C is then the resultant capacitance is

A sound wave of frequency 100 Hz is travelling in air. The speed of sound in air is 350 m s${}^{-1}$.

What is the phase difference at a given instant between two points separated by a distance of 10.0 cm along the direction of propagation?

A horizontal force just sufficient to move a body of mass $4\text{kg}$ lying on a rough horizontal surface is applied on it. The coefficient of static and kinetic friction between the body and the surface are $0.8$ and $0.6$, respectively. If the force continues to act even after the block has started moving, the acceleration of the block in ${\text{ms}}^{-2}$ is $(g=10{\text{ms}}^{-2})$

Find the acceleration of the two bodies ($A$ and $B$), if the system shown is initially at rest.
Take $g=10{\text{m/s}}^2$.

Volume of a given amount of gas at ${57}^{\circ }\text{C}$ is $425.8{\text{cm}}^3$. If the temperature is decreased to ${37}^{\circ }\text{C}$ at constant pressure, then the volume of the gas would be :

A river is flowing with a speed of $1\text{km/hr}$ as shown in figure. A swimmer wants to go to the point C starting from point A. He swims with a speed of $5\text{km/hr}$ with respect to the flowing river at an angle $\theta$ as shown. If $AB=BC=400\text{m}$, then value of $\theta$ is:

A projectile of mass $0.5kg$ is thrown with a velocity of $30m/s$ at an angle of ${60}^0$ with the horizontal. Find its momentum at highest point.

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. What is the maximum height attained by the ball?

One mole of ideal gas undergoes a linear process as shown in figure below. Its temperature expressed as a function of volume V is.

In Young’s double slit experiment, the two slits act as coherent sources of light waves of equal amplitude a and of wavelength $\lambda$. In another experiment with the same setup, the two slits are source of light waves of equal amplitude a and wavelength $\lambda$ but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is:

An aeroplane is travelling horizontally at a height of $2000\text{m}$ from the ground. The aeroplane, when at a point P, drops a bomb to hit a stationary target Q on the ground. In order that the bomb hits the target, what angle $\theta$ must the line PQ make with the vertical ? $[g=10m{s}^{-2}]$

In the circuit shown below, the current through 10$\Omega$ resistor is

The scale on a steel meter stick is calibrated at ${15}^{\circ }\text{C}$. Find the error in the reading of $60\text{cm}$ at ${27}^{\circ }\text{C}$. Given ${\alpha }_{\text{steel}}=1.2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$

A force vector appliedon a body is given by $\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}$ and acquires an acceleration $1m{s}^2$ Then the mass of the body is

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is

In the arrangement shown, neglect the mass of the ropes and pulley. What must be the value of $m$ to keep the system in equilibrium. There is no friction anywhere.
Given: For $M$, force acting down the plane is $Mg\sin {30}^{\circ }$.

A $1\mu F$ capacitor holding a charge of $1\times {10}^{-5}C$ is connected to a $10\Omega$ resistor via switch.

What current will flow after the switch is closed?

Two blocks of mass $5kg$ and $3kg$ are tied with a heavy rope of mass $2kg$. An external force of $200N$ is applied on $5kg$ block and the whole system accelerates upwards. Find the tension at the midpoint of the rope?
(Take $g=10m/s^2$)

A metal cube of length $10.0\text{mm}$ at $0^{\circ }\text{C}\left(273\text{K}\right)$ is heated to ${200}^{\circ }\text{C}\left(473\text{K}\right)$. Given its coefficient of linear expansion is $2\times {10}^{-5}{\text{K}}^{-1}$, the percent change in its volume is

A double star consists of two stars having mass M and 2M. The distance between their centre is equal to r. They revolve under their mutual gravitational interaction. Then which of the following statements is/are correct.

Two blocks of mass 4 kg and 2 kg are connected by a heavy string and placed on rough horizontal plane. The 2 kg block is pulled with a constant force to the right. The coefficient of friction between the blocks and the ground is 0.4. What is the value of so that tension in the string is constant throughout during the motion of the blocks: $(g=10m/s^2)$

Two resistors of resistance $3\Omega$ and $6\Omega$ are in parallel and the combination is in series with a $4\Omega$ resistor. A potential difference of 90V is applied across the network. The potential difference across the $4\Omega$ and the current in the $3\Omega$resistor are respectively,

One mole of an ideal monoatomic gas is taken through a cycle $a\to b\to c\to a$ as shown in the figure. Find the difference between maximum and minimum values of internal energy of the gas during the cycle.

A circuit consists of a $2\mu F$ capacitor connected through an a.c ammeter to an a.c. source of voltage given by $V=200\sqrt{2}sin(100t+\pi /3)$ where $V$ is volts and $t$ in seconds. The reading of the ammeter is

Four different independent waves are represented by
i) $y_1=a_{1}sin\omega t$
ii) $y_2=a_{2}sin2\omega t$
iii) $y_3=a_{3}cos\omega t$
iv) $y_4=a_{4}sin(\omega t+\frac{\pi }{3})$
With which two waves is the interference possible?

A body cools from ${80}^{\circ }C$ to ${50}^{\circ }C$ in 5 minutes. Calculate the time it takes to cool from ${60}^{\circ }C$ to ${30}^{\circ }C$. The temperature of the surrounding is ${20}^{\circ }C.$

Refer to the previous problem. Suppose, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament. Calculate the volume of the cavities left that will allow the weights given in that problem.

For the given uniform square lamina $ABCD$, whose centre is $O$

A concave meniscus is observed for a liquid kept in a capillary tube, then angle of contact can be

The unit of surface tension in the $\text{CGS}$ system is

Three blocks with masses $m,2m$ and $3m$ are connected by strings, as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward at constant speed $v$. What is the net force on the block of mass $2m$?
($g$ is the acceleration due to gravity)

Light strikes a sodium surface, causing photoelectric emission. The stopping potential for the ejected electrons is 5.0 V, and the work function of sodium is 2.2 eV. What is the wavelength of the incident light? __nm.

The efficiency of heat engine is maximum when:

A light and a heavy body have equal momenta. Which one has greater K.E

If light is a electromagnetic wave, will it get deflected near a magnet ?

Q. A wire of length L and resistance R is stretched to get the radius of cross section halved. What is the new resistance of the wire ?

Two particles move along x axis. the position of particle 1 is given by x = 6.00$t^2$ + 3.00t + 2.00 (in meters and seconds); the acceleration of particles 2 is given by a = -8.00t ( in meters per second squared and seconds) and, at t = 0, its velocity is 19 m/s. When the velocities of the particles match, what is their velocity?

A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

In a Michelson experiment for measuring speed of light, the distance travelled by light between two reflections from the rotating mirror is 4.8 km. The rotating mirror has a shape of a regular octagon. At what minimum angular speed of the mirror (other than zero) the image is formed at the position where a nonrotating mirror forms it?

A cyclic process for $1$ mole of an ideal gas is shown in figure in the $V-T$ diagram. The work done in process $AB,BC$ and $CA$ respectively, are

At what absolute temperature $T$ is the root mean square speed of a hydrogen molecule equal to its Escape velocity from the surface of the moon? The radius of moon $R=g$ is the acceleration due to gravity on moon's surface $m$ is the mass of a hydrogen molecule and $k$ is the Boltzmann constant

If the pressure amplitude in a sound wave is tripled, then the intensity of

sound is increased by a factor of