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Consider the situation shown in figure. Initially, the spring is unstretched when the mass $m$ is released from rest. Assuming no friction in the pulley, find the maximum extension in the spring.

When a certain photosensitive surface is illuminated with monochromatic light of wavelength $\lambda$, the stopping potential for photoelectric current is $2V_0$. When the same surface is illuminated with monochromatic light of wavelength $2\lambda$, the stopping potential is $\frac{V_0}{2}$. The threshold wavelength for photoelectric emission is

A concave mirror of focal length $10\text{cm}$ produces an image which can be obtained on the screen. If the image size is four times the size of the object, the distance of object from the pole of the mirror is

If $x,v$ and $a$ denotes the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T$. Then which of the following does not change with time?

Choose the correct option based on the prallelogram $ABCD$.

A particle is thrown upwards such that its maximum height is $4h$. The height of the particle where speed is $3/4^{th}$ of the maximum speed is

A wire is bent in the form of a circular arc with a straight portion AB. Magnetic field at O when current $I$ is flowing in the wire is

A body of mass $2\text{kg}$ is attached to a light rod of length $5\text{m}$ and is allowed to move in a vertical circle. The body is given an initial velocity of $u\text{m/s}$ at the bottom-most point, such that the final velocity at the top-most point is zero. The value of $u$ is

Find the ratio of moment of inertia of a ring and a disc about an axis passing through their center and perpendicular to their plane. Both ring and disc have the same mass and same radius.

In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be

A particle moves from A to B along the semicircular curve as shown in the figure. The ratio of distance covered by particle to its displacement is

Three sources of sound $S_1,S_2$ and $S_3$ of equal intensity 'I' are placed in a straight line with $S_1{S}_2=S_2{S}_3$. At a point P, far away from the sources, the wave coming from $S_2$ is ${120}^{\circ }$ ahead in phase of that from $S_1$. Also, the wave coming from $S_3$ is 120° ahead of that from $S_2$. What would be the resultant intensity of sound at P?

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The $\gamma$ of the gas is

An engine of a train, moving with uniform acceleration, passes the signal post with velocity $u$ and the last compartment passes the signal post with velocity $v$. The velocity with which the middle point of the train passes the signal post is :

A loaded vertical spring executes simple harmonic oscillations with period of 4 s. The difference between the kinetic energy and potential energy of this system oscillates with a period of

An X-ray photon of wavelength $\lambda$ and frequency $v$ collides with an electron and bounces off. If ${\lambda }^{\prime }$ and $v^{\prime }$ are respectively the wavelength and frequency of the scattered photon, then

Three bodies of mass $1\text{kg},2\text{kg}$ & $4\text{kg}$ have position vectors $3\hat{i},2\hat{i}-\hat{j},2\hat{i}+\hat{j}$ respectively. Then, centre of mass of this system has a position vector :

On a new scale of temperature (which is linear) and called the $W$ scale, the freezing and boiling points of water are ${42}^{\circ }\text{W}$ and ${242}^{\circ }\text{W}$ respectively. What will be the temperature on the new scale, corresponding to the temperature of ${42}^{\circ }\text{C}$ on the Celsius scale ?

[CPMT 1988; KCET 1998; UPSEAT 2001]

In the given figure $V_B$ is (All surfaces are smooth and string is massless and inextensible)

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



Neglect density of air compared to that of oil. (Viscosity of air $=\frac{18\times {10}^{-5}}{5}{\text{N.s/m}}^2,g=10{\text{m/s}}^2$, density of oil $=900{\text{kg/m}}^3$

A body floats in water with one-third of its volume above the surface of water. If it is placed in oil, it floats with half of its volume above the surface of the oil. The relative density of the oil is

In a hydraulic lift, compressed air exerts a force $F_1$ on a small piston having a radius of $5\text{cm}$. This pressure is transmitted to a second piston of radius $15\text{cm}$. If the mass of the load to be lifted is $1350\text{kg}$, calculate the pressure acting on the smaller piston.

[Take $g=10{\text{m/s}}^2$]

A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the distance between two points on a wave whose phase difference is ${45}^{\circ }.$

A parallel-plate capacitor with plate area A and separation between the plates d is charged by a constant current i. Consider a plane surface of area $\frac{A}{2}$ parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.

A rifle bullet loses $1/{20}^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.

The curve between charge density and distance near P-N junction will be

Which of the following figures represents damped harmonic motion?

If $\overrightarrow{B}$ makes an angle of ${53}^{\circ }$ and $\overrightarrow{C}$ makes an angle of ${37}^{\circ }$ with $x-$axis as shown in the figure and the magnitude of $\overrightarrow{A}$ and $\overrightarrow{C}$ is equal to $10$ and $5$ respectively, then the magnitude of $\overrightarrow{B}$ is [Given, $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=0$] (Take $\sqrt{9804}=99)$

Find the average velocity of tip of the minute hand of an analog watch when it turn for $15\text{minutes}$.

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are three mutually perpendicular unit vectors, then $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|$ is equal to

A ball is thrown up from the top of a tower with 20 m/s velocity. It took the ball 6 sec to fall to the bottom. How much distance did the ball cover in the last second of its motion?

The displacement of a particle of a string carrying a travelling wave is given by $y=3\sin \left[6.28\right(0.50x-50t\left)\right]$

$(x\to \text{in cm},y\to \text{cm},t\to \text{in second})$.

What would be the speed of the wave?

If $A=3\hat{i}+4\hat{j}$ and $B=7\hat{i}+24\hat{j}$, the vector having the same magnitude as B and parallel to A is

A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity $v=(5t\hat{i}+2t\hat{j})\text{m/s}$. Here $t$ is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take $g=10m/s^2$)

A car and a truck move in the same straight line at the same instant of time from the same point. The car moves with a constant velocity of $40\text{m/s}$ and truck starts with a constant acceleration of $4{\text{m/s}}^2$. Find the time $t$ that elapses before the truck catches with the car and also find the greatest distance $S_{max}$ between them prior to it

A curved mirror converges a parallel beam of light incident on it to its focus, the mirror is

Calculate the moment of Inertia of a solid cylinder of mass '$M$' and radius $R$ about its Axis(as shown)?

List I gives some physical quantites, and List II gives some possible graphs



symbols have usual meaning i.e., a, v, x, t stands for acceleration, velocity, position and time. For given v - t graph correct match is? Where at t = 0, particle is at some positive position

The component of vector $A=2\hat{i}+3\hat{j}$ along the vector

$\hat{i}+\hat{j}$ is

Calculate Reynold's number if a fluid having a viscosity of $0.25{\text{N.s/m}}^2$ and density of $800{\text{kg/m}}^3$ flows through a pipe of radius $10\text{mm}$ with a velocity of $2\text{m/s}$.

From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the

same siren. The ratio of velocity of train B to that of train A is

An air bubble in a glass slab $(\mu =1.5)$ is 6 cm deep when viewed from one face and 4 cm deep when viewed from the opposite face. The thickness of the glass plate is3

Boolean algebra is essentially based on ?