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A block mass $M=5kg$ is moving on a horizontal plane and an object of mass $m=1kg$ is dropped on to the block hitting it with a vertical velocity of $v_1=10m/s$. If the speed of the block at the same instant is $v_2=2m/s$ on the floor and collision is momentary and the object sticks to the block on collision. Then what will be the speed of the block just after the collision if the coefficient of friction between the block and the horizontal plane is 0.4 ?

Continuous X -rays are made to strike a tissue paper soaked with polluted water. The incoming X-rays excite the atoms of the sample by knocking out the electrons from the inner shells. Characteristic X-rays are subsequently emitted. The emitted X-rays are analysed and the intensity is plotted against the wavelength figure. Assuming that only $K_{\alpha }$ intensities are detected, list the elements present in the sample from the plot. Use Moseley's equation

A resistor of resistance 100 $\Omega$ is connected to an AC source $\epsilon$ = (12 V) sin $\left(250\pi s^{-1}\right)$t. Find the energy dissipated as heat during t = 0 to t = 1.0 ms.

When the momentum of a proton is changed by an amount $P_0$, the corresponding change in the de-Broglie wavelength is found to be $0.25\%$. Then, the original momentum of the proton was

Find the binding energy per nucleon of ${}_{79}^{197}$Au if its atomic mass is 196.96 u.

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:

${}^{12}\text{N}{\to }^{12}{\text{C}}^{\ast }+e^{+}+v$

${}^{12}{\text{C}}^{\ast }{\to }^{12}\text{C}+v\left(4.43\text{MeV}\right)$

A force is inclined at ${60}^{\circ }$ to the horizontal produces a displacement of $\overrightarrow{s}=(\hat{i}+\hat{j})\text{m}$. If the component of force in horizontal direction is $50\text{N}$, the net work done by the force on the body is

The potential energy of a particle varies with distance $x$ as $\frac{A{x}^{1/2}}{x^2+B}$, where $A$ and $B$ are constants. The dimensional formula for $A\times B$ is

The figure below shows the path of white light’s rays which leave in phase from two small sources $S_1$ and $S_2$ and travel to a point X on a screen. The path difference is $S_{2}X-S_{1}X=8.7\times {10}^{-7}m$. What wavelength of light gives complete destructive interference at X?

The first overtone frequency of a closed organ pipe $P_1$ is equal to the fundamental frequency of an open organ pipe $P_2$. If the length of the pipe $P_1$ is $60\text{cm}$, what will be the length of $P_2$?

A person siting on the top of a ball building is dropping balls at regular intervals of one second. Find the positions of the 3rd, 4th and 5th ball when the 6th ball is being dropped.

If air resistance is taken into consideration when the body is projected at an angle then which of the following is correct

1. The time taken to move to Maximum height if greater than the time taken to move from Maximum height to the ground

2. At maximum height acceleration of projectile is greater than g

3. Maximum height decreases

4. Speed of the projectile when it hits the ground is equal to the speed of projection

A perfect gas goes from state $A$ to another state $B$ by absorbing $8\times {10}^5\text{J}$ of heat and doing $6.5\times {10}^5\text{J}$ of external work. The change in internal energy will be

In a sample of an ideal gas the average momentum of a molecule depends on

A particle executes simple harmonic motion along a straight line with an amplitude A. The potential energy is maximum when the displacement is

The momentum of a photon is $2\times {10}^{-16}gm-cm/sec$. Its energy is

If $F_1=5\text{N}$ and $F_2=10\text{N}$ as shown in the figure, the resultant $R$ will be [Hint: $\cos {65}^{\circ }=0.423$]

The two blocks in an Atwood machine have masses 2.0 kg and 3.0 kg. Find the work done by gravity during the fourth second after the system is released from rest.

You have prepared a nice sample of $N_{\circ }$ radioactive nuclei of decay constant $\lambda$, and want to show it off to your friends. When they arrive units of time later, you open the lid and find there are only _______ nuclei left intact.

The half-life of ${}^{198}Au$ is 2.7 days. Calculate the decay constant.Take atomic weightof ${}^{198}Au$ to be 198 g $mo{l}^{-1}$

Figure shows a cylindrical tube of radius 5 cm and length 20 cm. It is closed by a tight-fitting cork. The friction coefficient between the cork and the tube is 0.20. The tube contains an ideal gas at a pressure of 1 atm and a temperature of 300 K. The tube is slowly heated and it is found that the cork pops out when the temperature reaches 600 K Let dN denote the magnitude of the normal contact force exerted by a small length dl of the cork along the periphery (see the figure). Assuming that the temperature of the gas is uniform at any instant, calculate $\frac{dN}{dl}$.

A solid body starts rotating about a stationary axis with an angular acceleration = $at$. How soon after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle = ${60}^{\circ }$ with its velocity vector?

A block of mass 2.0 kg is pushed down an inclined place of inclination ${37}^{\circ }$ with a force of 20 N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of 10 $m/s^2$. If the block started from rest, find the work done (a) by the applied force in the first second, (b) by the weight of the block in the first second and (c) by the frictional force acting on the block in the first second. Take g=$10m/s^2$.

A block is sliding along incline as shown in the figure. If the acceleration of the chamber is $a$ as shown in the figure. The time required to cover a distance $L$ along the incline is:

A projectile is thrown upwards with a velocity v at an angle theta with the vertical.Its average velocity between the instants it crosses half the maximum height is:

A point moves with uniform acceleration and $v_1,v_2$ and $v_3$ denote the average velocities in the three successive intervals of time $t_1,t_2$ and $t_3$. Which of the following relations is correct?

The radius of gyration of a uniform rod of length $L$ about an axis passing through its centre of mass is

As shown in figure, a ring of radius $R$ is rolling without slipping. What will be the magnitude of velocity of point $A$ on the ring ?

A simple pendulum of period T has a metal bob which is negatively charged. If it is allowed to oscillate above a large positively charged metallic plate, its period of oscillation will be,

I have an insulator with dielectric constant k. If I place it in a region in vacuum with a field E, what is the induced field inside the dielectric?

A square loop of side 4 cm is lying on a horizontal table. A uniform magnetic field of 0.5 T is directed downwards at an angle of ${60}^o$ to the vertical as shown in Fig. 25.3. If the field increases from zero to its final value in 0.2 s, the emf induced in the loop will be

Which instrument does C play?

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = a) is

[MP PMT 1987; CPMT 1990; DPMT 1996;

MH CET 1997, 99; AFMC 1999; CPMT 2000]

A ball hits the floor and rebounds after inelastic collision. In this case

Length of a string of density ρ and Young’s modulus Y under tension is increased by $\frac{1}{n}$ times of its original length. If the velocity of transverse and longitudinal vibrations of the string is same, find the value of such velocity.

The specific heat of one mole of an ideal `gas at constant volume is $21.2J/mole{/}^{\circ }C$. If the temperature is increased by $1^{\circ }C$ keeping the volume constant, the change in its internal energy will be

A glass vessel measures exactly 10 cm $\times$ 10 cm $\times$ 10 cm at $0^{\circ }C$. It is filled completely with mercury at this temperature. When the temperature is raised to ${10}^{\circ }C$, $1.6c{m}^3$ of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass $=6.5\times {10}^{-6}{}^{\circ }{C}^{-1}$.

A rod of uniform mass 2kg has a length of 5m. What will be its moment of inertia about a line perpendicular to the rod and passing through its middle point?

Calculate the current through the circuit and the potential difference across the diode shown in figure (45-E1). The drift current for the diode is $20\mu A.$

Two particles, one with constant velocity $50{\text{m s}}^{-1}$ and the other with uniform acceleration $10{\text{m s}}^{-2}$, start moving simultaneously from the same place in the same direction. They will be at a distance of 125 m from each other after

The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude, is

The maximum speed of particle in S.H.M is p and maximum acceleration of particle in S.H.M is q, then time period of particle is

A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at thr other end Figure. Shoe that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.