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The work function of a metal is $1.6\times {10}^{-19}J$. When the metal surface is illuminated by the light of wavelength $6400\stackrel{\circ }{A}$ , then the maximum kinetic energy of emitted photo-electrons will be (Planck's constant $h=6.4\times {10}^{-34}Js$)

When a capillary tube is dipped in a liquid, liquid rises $0.06\text{m}$ in it. Surface tension of liquid is $0.03\text{N/m}$, density of liquid is ${10}^3{\text{kg/m}}^3$. If contact angle is ${60}^{\circ }$, then radius of capillary is (Assume $g=10{\text{m/s}}^2$)

Two parallel-plate capacitors of capacitance $C$ and $2C$ are connected in parallel and charged to a potential difference $V$. The battery is then disconnected and the region between the plates of capacitor $C$ is filled completely with a material of dielectric constant $K$. The common potential difference across the combination becomes

An ice cube of mass $0.1\text{kg}$ at $0^{\circ }\text{C}$ is placed in an isolated container which is at ${227}^{\circ }\text{C}$. The specific heat $S$ of the container varies with temperature $T$ according to the empirical relation $S=A+BT$, where $A=100\text{cal/kg K}$ and $B=2\times {10}^{-2}{\text{cal/kg K}}^2$. If the final temperature of the container (with the material in it) is ${27}^{\circ }\text{C}$, determine the mass of the container.

[Latent heat of fusion of water $=80{\text{cal/g}}^{\circ }\text{C}$, specific heat of water $=1{\text{cal/g}}^{\circ }\text{C}$]

A right-angled prism of apex angle $4^{\circ }$ and refractive index $1.5$ is located in front of a vertical plane mirror as shown in figure. A horizontal ray of light is falling on the prism. Find the total deviation produced in the light ray as it emerges 2nd time from the prism.

If in a wire of Young's modulus $Y$, longitudinal strain $X$ is produced, then the elastic potential energy stored in its unit volume will be

In the figure shown, the particles have charges $q_1$ = $-q_2$ = 300 nC and $q_3$ = $-q_4$ =200 nC, and distance a = 5.0 cm. What are the (A) magnitude and (B) angle (relative to the +x direction) of the net force on particle 3?

A force $\overrightarrow{F}=-K(y\hat{i}+x\hat{j})$ (where K is a positive constant) acts on a particle moving in the x - y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force on the particle is

In an elastic collision of two particles the following is conserved

A particle of mass $2\text{kg}$ is projected on horizontal ground with an initial velocity $u=20\text{m/s}$ making an angle ${60}^{\circ }$ with the vertical. Find out the angular momentum of the particle about the point of projection when it just strikes the ground. [in ${\text{kg m}}^2\text{/s}$]

Find the maximum mass $m_2$ that can be hanged from the pulley such that the system remains in equilibrium. Coefficient of friction between block $m_1$ & wedge is $mu$.

If frame of reference is changed, which quantity may change its value ?

A hollow sphere of mass 50 kg and radius 5 cm is rotated about one of its diameter. The rotational inertia of hollow sphere about this axis is.

A particle of mass $m$ moving in the $x-$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y-$ direction with speed $v$. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

The spring shown in figure is kept I a stretched position with extension $x_0$ when the system is released. Assuming the horizontal surface to be frictionless, find the frequency of oscillation.

For a spring block system as shown in figure, a time varying force $F=5t\text{N}$ is applied on mass $2\text{kg}$. After $10\text{seconds}$, velocity of $3\text{kg}$ mass is $30\text{m/s}$. Find the velocity of $2\text{kg}$ mass at this instant.

The lower surface of the cube floating in water just touches the free end of a vertical spring fixed at the bottom of the vessel. The maximum weight that can be put on the block without wetting it is-

A rectangular plate of mass $m=3\text{kg}$ having sides $a=4\text{m}$ and $b=2\text{m}$ is placed on XY plane as shown in figure. Find the moment of inertia of rectangular plate about an axis passing through the point ${}^{\prime }{O}^{\prime }$ and perpendicular to its plane.

Which of the following graphs correctly represents the variation of molar heat capacity at constant volume with temperature for an ideal monoatomic gas?

Consider two observers moving with respect to each other at a speed v along a straight line. They observe a block of mass m moving a distance l on a rough surface. The following quantities will be same as observed by the two observers.

A bullet moving with a velocity of $100\text{m/s}$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet, when the velocity is doubled, will be -

A person can see clearly only up to a distance of $30\text{cm}$. He wants to read a book placed at a distane of $50\text{cm}$ from his eyes. What is the power of the lens he requires for his spectacles?

Which of the following graph shows the relation between shear stress and velocity gradient for a non-Newtonian fluid?

Find the equivalent resistance between A and E (Resistance of each resistor is R).

A car accelerates uniformly from $13\text{m/s}$ to $31\text{m/s}$ while entering the motorway, covering a distance of $220\text{m}$. Then the acceleration of the car will be:

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

A mass M is suspended by a rope from a rigid support at P as shown in the figure. Another rope is tied at the end Q, and it is pulled horizontally with a force F. If the rope PQ makes angle $\theta$ with the vertical then the tension in the string PQ is

A closed organ pipe of length $10\text{cm}$ has fundamental frequency equal to half the value of the second overtone of an open organ pipe. The length of the open organ pipe will be

The work function of aluminium is 4.2 eV. If two photons, each of energy 3.5 eV strike an electron of aluminium, then emission of electrons will be

An express train is moving with a velocity $v_1$. Its driver finds another train is moving on the same track in the same direction with velocity $v_2(v_2<v_1)$. To escape collision, the driver applies a retardation $a$ on the train. The minimum time to escape the collision is

An oil drop falls through air with a terminal velocity $5\times {10}^{-4}\text{m/s}$. Find the radius of the drop.

Neglect the density of air as compared to that of oil. (Take viscosity of air $=3.6\times {10}^{-5}{\text{N-s/m}}^2,g=10{\text{m/s}}^2$, density of oil ${\rho }_o=900{\text{kg/m}}^3)$

In an experiment on photoelectric effect, the emitter and the collector plates are placed at a separation of 10 cm and are connected through an ammeter without any cell. A magnetic field B exists parallel to the plates. The work function of the emitter is 2.39 eV and the light incident on it has wavelengths between 400 nm and 600 nm. Find the minimum value of B for which the current registered by the ammeter is zero. Neglect any effect of space charge.

Air is streaming past a horizontal air plane wing such that its speed is 120m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per $metr{e}^3$ and the wing is 10 m long and has an average width of 2 m, then the difference of the pressure on the two sides of the wing is

Corresponding to point A on acceleration time (a-t) curve of a particle executing SHM, there is a point 1 or 2 or 3 or 4 on velocity time (v-t) curve of the motion. The starting value of time on x-axis is different for two curves. Find the point:

An object is displaced from position ${\overrightarrow{r}}_1=\hat{i}+2\hat{j}\text{m}$ to $\overrightarrow{r_2}=2\hat{i}+4\hat{j}\text{m}$ under the action of force $\overrightarrow{F}=(6x^2\hat{i}+4y\hat{j})\text{N}$. Find the work done by this force.

A particle is projected from the bottom of an inclined plane of inclination ${30}^{\circ }$ (with the horizontal) with speed $40\text{m/s}$ at an angle ${60}^{\circ }$ with the horizontal. The speed of the particle when its velocity vector is parallel to inclined plane is $(g=10{\text{m/s}}^2)$

A ball of mass $20\text{kg}$ is suspended from a massless string of length $5\text{m}$ as shown in figure. A bullet of mass $5\text{kg}$ moving with velocity $v_0\text{m/s}$ collides with the ball and sticks to it. Find the minimum value of $v_0$ so that the combined mass completes the vertical circular motion. [Take $g=10{\text{m/s}}^2$]

Which of the following set of forces

cannot keep a body in equilibrium?

Two capillary tube of radius $r_1$ and $r_2$ are put vertically one each in two liquids whose relative densities are $0.6$ and $0.4$ and surface tension are $60\text{dyne/cm}$ and $50\text{dyne/cm}$ respectively.

If ratio of heights of liquid in two tube is $8:10$ respectively. Find $\frac{r_1}{r_2}$.

(Assume contact angle is same in both case)

A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of length 850 meters is

A particle starts from the origin of co-ordinates at time $t=0$ and moves in the $xy$ plane with a constant acceleration $\alpha$ in the $y$ – direction. Its equation of motion $y=\beta x^2$. Its velocity component in the $x$-direction is

A plane mirror is moving with velocity $(4\hat{i}+5\hat{j}+7\hat{k})\text{m/s}$. A point object in front of the mirror moves with a velocity $(3\hat{i}+4\hat{j}+5\hat{k})\text{m/s}$. Here $\hat{k}$ is along the normal to plane mirror and facing towards the object. The velocity of image w.r.t ground is (in SI units)

Figure represents a glass plate placed vertically on a horizontal table with a beam of unpolarised light falling on its surface at the polarising angle of 57^o with the normal. The electric vector in the reflected light on screen S will vibrate with respect to the plane of incidence in a

[CPMT 1988]

What is the angle between $\overrightarrow{P}$ and the resultant of $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}-\overrightarrow{Q})$

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is

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

Statement I: A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving a certain distance. The surface is now tilted to an angle of ${30}^{\circ }$ with the horizontal, and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

Statement II: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

A gun fires $10$ bullets/sec each of mass $10gm$, with a muzzle velocity of $50m/s$. Find the force required to hold the gun in position.