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Two identical blocks $A$ and $B$, connected through a massless string are placed on a frictionless horizontal surface. A bullet having mass $2$ times that of a single block, moving with velocity $u$ strikes block $B$ from behind as shown in the figure. If the bullet comes to rest after striking the block, find the impulse on block $A$ due to tension in the string.

If the image of a stone placed infront of a mirror is seen by the observer 1 at position C, then where will the observer 2 see the image?

A rod of length $10\text{m}$ is placed in vertical direction. Then the rod is rotated by ${90}^{\circ }$ in clockwise direction. Find out the displacement of the $COM$ of the rod.

The relation between the gas pressure P and average kinetic energy per unit volume E is

There are found X-Rays with energy ranging from 2 KeV to 5 KeV. What is the minimum and maximum wavelength of X- Ray photon present respectively? (Take hc to be 1242 eV-nm)

In the figure shown, a body of mass $6kg$ is at a distance of $16m$ from the pulley at $t=0$ when it is released. If the string is cut after $2s$, then find the time after which the $6kg$ block will hit the pulley. Consider the surface to be smooth (Take $g=10m/s^2$)

Natural length of a massless spring (of spring constant $k$) is $x$. It is slowly stretched by applying an external force. What is the work done in slowly increasing its extension from $3x$ to $4x$?

The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 seconds, it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is

A large body of mass 100 kg moving with a velocity of 10.0 m/s collides elastically with a small body of mass 100 g at rest. The velocity of the small body is

A projectile is thrown from the ground with an initial velocity of $(4\hat{i}+3\hat{j})$$m/s$. It reaches its greatest height above the ground after (Take $g=10m/s^2$)

Two oscillating systems; a simple pendulum and a vertical spring - mass - system have same time period of motion on the surface of the Earth. If both are taken to the moon, then

A plane is flying horizontally at $98m/s$ and releases an object which reaches the ground in 10 seconds. The angle made by it when it hits the ground is

If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect

An object of mass $8\text{kg}$ falls through a height of $60\text{m}$ and by means of a mechanical linkage, rotates a paddle wheel that stirs $0.8\text{kg}$ of water. Determine the change in temperature of water if initial temperature was ${15}^{\circ }\text{C}$. Assume no heat is lost to surroundings, specific heat of water, $c=4190\text{J/kg}{}^{\circ }\text{C})$.

A uniform chain of mass $m$ and length $L$ hangs on a table with two thirds of its length on the table. The work done by a person to put the hanging part back on the table will be

In a charged capacitor, the energy resides as

A body is moving in a straight line, starting its journey from origin. At any instant, its velocity is given by,$K_1{t}^{(K_1-1)}$ when $K_1$ is a constant and t is the time. Find the acceleration of the particle, when it is at a distance s from the origin:

Find tension in the left and the right string?

The minimum energy required to remove an electron is called

A metallic sphere floats in an immiscible mixture of water (density 10${}^3$ kg/m${}^3$) and a liquid (density $8\times {10}^{3}kg/m^3$) such that its ($\frac{2}{3}$) part is in water and ($\frac{1}{3}$) part in the liquid. The density of the metal is

The value of ${\int }_1^5{x}^{2}dx$ is

A uniform solid sphere of radius $R$ and mass $m$ rolls down an inclined plane. The coefficient of friction between the sphere and the inclined plane is $\mu$ then maximum value of $\theta$ for pure rolling is

Two spherical bodies $A$ and $B$ with a radius of $12\text{cm}$ and $18\text{cm}$ respectively are at temperatures $T_A$ and $T_B$. The maximum intensity in the emission spectrum of $A$ is at $1000\text{nm}$ and in that of $B$ is at $2000\text{nm}$. Considering both bodies to be black bodies, Find the ratio of the rate of total energy radiated by $A$ to that of $B$ ?

A small ball of density $\rho$ is immersed in a liquid of density $\sigma (>\rho )$ to a depth h and released. The height above the surface of water up to which the ball will jump is

A car travels at a constant speed of $30\text{m/s}$ around a level circular bend of radius $100\text{m}$. What is the minimum coefficient of static friction between the tires and the road in order for the car to go round the bend without skidding?

Find the integral of the given function w.r.t x

$y=sin\left(8x\right)+x$

The photo-electrons emitted from a surface of sodium metal are such that

The acceleration of a train travelling with speed of 400 m/s as it goes round a curve of radius 160 m, is

The rates of cooling of two different liquids put in exactly similar calorimeters and kept in identical Surroundings are the same if

A wire $40cm$ long is bent into a rectangular frame $15cm\times 5cm$ and placed perpendicular in a magnetic field intensity of $0.8T$ . The frame is changed into a square frame and the field is increased to $1.4T$ in a time interval of $0.5s$. The e.m.f induced in the frame is ________.

In a common emitter transistor amplifier the audio signal voltage across the collector is 3V. The resistance of collector is $3k\Omega$. If current gain is 100 and the base resistance is $2k\Omega$, the voltage and power gain of the amplifier is

A gate has the following truth table

P 1 1 0 0

Q 1 0 1 0

R 1 0 0 0

The gate is

Block $A$ of mass $\frac{m}{2}$ is connected to one end of a light rope which passes over a light frictionless pulley as shown in figure.





A man of mass $2m$ climbs the other end of the rope with a relative acceleration of $\frac{g}{2}$ with respect to rope. Find the acceleration ($a_0$) of block $A$ with respect to ground.

A car moving on a horizontal road may be thrown out of the road in taking a turn

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of the materials, then

A string of length $7\text{m}$ has a mass of $0.035\text{kg}$. If the tension in the string is $60.5\text{N}$, then speed of a wave on the string is:

Vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ makes angle of ${20}^{\circ }$ and ${110}^{\circ }$ respectively with $+x$-axis. The magnitude of these vectors are $5\text{m}$ and $12\text{m}$ respectively. Then the magnitude of the resultant vector is

Let $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$ then

A uniform rod of length $l$ & mass $M$ is free to rotate about frictionless pin through one end. The rod is released from rest in a horizontal position. Find momentum of system (rod) when rod is at its lowest position.

A pn junction (D) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit.



The current (I) in the resistor R can be shown by

What happens to the centripetal acceleration of a revolving body if you double the orbital speed v and half the angular velocity $\omega$

In a gravity free space, a particle is connected with four springs as shown below. If the particle is pulled down gently and left, then find the period of oscillation of the particle.

$(\text{Given}:\theta ={45}^{\circ },\beta ={30}^{\circ })$

What is the minimum value of $F$ needed so that block begins to move upward on frictionless incline plane as shown?

Two identical metal plates show photoelectric effect by a light of wavelength ${\lambda }_A$ falls on plate A and ${\lambda }_B$ on plate B $({\lambda }_A=2{\lambda }_B)$. The maximum kinetic energy is

One end of a long metallic wire of length L, area of cross-section A and Young’s modulus Y is tied to the ceiling. The other end is tied to a massless spring of force constant k. A mass m hangs freely from the free end of the spring. It is slightly pulled down and released. Its time period is given by

A uniform bar with mass $m$ lies symmetrically across two rapidly rotating fixed rollers A and B, with distance ${}^{\prime }{l}^{\prime }$ between the bar's centre of mass and each roller. The rollers whose direction of rotation are shown in figure slip against the bar with coefficient of friction $\mu$. Suppose the bar is displaced horizontally by a small distance ${}^{\prime }{x}^{\prime }$ and then released, find the time period of oscillation.

The density of a linear rod of length $L$ varies as $\rho =A+Bx$ where $x$ is the distance from the left end. Its centre of mass is at a distance (from the left end) of