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A particle performing SHM has a velocity $v_0$ at mean position. Find the velocity of the particle, when it reaches a point which is at a distance $\frac{A}{2}$ from the mean position.

[$A=$ amplitude of SHM]

A boy is sitting on a swing at a maximum height of 5m above the ground. When the swing passes through the mean position which is 2m above the ground his velocity is approximately

In the arrangement shown in the figure, accelerations of blocks $A,B$ and $C$ are $a_A,a_B$ and $a_C$ respectively. Consider string and pulley to be mass-less and friction absent everywhere in the arrangement. Then

A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects, each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity of

A sample of ideal gas at ${100}^{\circ }\text{C}$ and normal pressure $(1.03\times {10}^5{\text{Nm}}^{-2})$ absorbs $54\text{cal}$ of heat energy at constant pressure. If the volume of the gas increases by $167\text{cc}$, the change in internal energy of the sample is :

Two bodies A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface areas of the two bodies are the same . The two bodies emit total radiant power at the same rate. The wavelength ${\lambda }_B$ corresponding to maximum spectral radiancy in the radiation from B shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from A, by 1.00 $\mu m$. If the temperature of A is 5802 K

A steel rod is 3.000 cm in diameter at ${25}^{\circ }C$. A brass ring has an interior diameter of 2.992 cm at ${25}^{\circ }C$. At what common temperature will the ring just slide on to the rod.

${\alpha }_{steel}=12\times {10}^{-6}{K}^{-1}$ and

${\alpha }_{brass}=18\times {10}^{-6}{K}^{-1}$

A gun fires a bullet of mass $50\text{g}$ with a velocity of $30\text{m/s}$. Due to this, the gun is pushed back with a velocity of $1\text{m/s}$, then the mass of the gun is:

A car, moving with a speed of $50km/hr$, can be stopped by brakes after at least $6m$. If the same car is moving at a speed of $100km/hr$, the minimum stopping distance is

In the following, which one of the diodes is reverse biased?

A ball is thrown vertically upward and its motion is studied before it falls on the ground. Which of the following represents velocity time graph of the ball during its flight (air resistance is neglected)

The position of the particle is given by $x=3t^2-6t+4$ in $\text{m}$. The acceleration of the particle at $10\text{sec}$ is

A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was 4D, the power of a cut-lens will be

For small oscillations, a pendulum of length L is released from rest. Its length is L and time period is T. vertically below the point of suspension O, there is an obstacle P at a vertical distance x. the pendulum returns back to its original position after time $\frac{5T}{8}$. Find x.

A particle is projected at an angle of ${37}^{\circ }$ with an inclined plane. The inclined plane is at an angle of ${60}^{\circ }$ with the horizontal. Find

I. Time of flight of particle.

II. Distance traveled by particle (AB) along the inclined plane

A smooth block of mass $10\text{kg}$ is released from rest from a height $5\text{m}$. It slides and compresses the spring of stiffness as shown in figure $200\frac{\text{N}}{\text{m}}.$ The maximum compression of the spring is

A small metal sphere, carrying a net charge of $q_1=-2\mu C$, is held in a stationery position by insulating supports. A second small metal sphere, with a net charge of $q_2=-8\mu C$ and mass $1.50g$ is projected towards $q_1$. When the two spheres are $0.800\text{m}$ apart, $q_2$ is moving towards $q_1$ with speed $20m{s}^{-1}$ as shown in the figure. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.

How close does $q_2$ get to $q_1$?

If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are $a,b$ and $c$ respectively, then the corresponding ratio of increase in their lengths would be

A motorboat going downstream overcame a raft at a point A; t = 60 minutes later, it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

The velocity of a body of mass $2kg$ varies according to the equation $v=(10S–3)m/s$ where $S$ is the displacement of the body (in $m$). Find the force acting on the body at the instant when it has undergone a displacement of $2m$.

If force $F$ is applied for stretching a wire of length $L$ by $\Delta L$, then elastic potential energy stored per unit volume is

($A$ is cross sectional area of wire)

In the figure shown, find the tension $T_1$, if all surfaces are smooth. Take $g=10{\text{m/s}}^2$.

Four identical samples of an ideal gas are taken along the paths $A,B,C$ and $D$ from state $1$ to state $2$ as shown in the $PV$ indicator diagram. Let $Q,W$ and $\Delta U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

Two tuning forks when sounded together produced a beat with frequency of 4 Hz. The frequency of one fork is 256 Hz. The number of beats heard increases when the fork of frequency 256 Hz is loaded with wax. The frequency of the other fork is,

A square plate of edge $\frac{a}{2}$ is cut out from a uniform square plate of edge ${}^{\prime }{a}^{\prime }$ as shown in the figure. The mass of the remaining portion is $M$. The moment of inertia of the remaining portion about an axis passing through $\text{'O'}$ (centre of the square of side $a$) and perpendicular to the plane of the plate is:

In which of the following situations, the transistor is operating in the active region ?

A ball is projected down the incline plane with velocity $u$ at right angle to the plane which is inclined at an angle $\alpha$ with the horizontal. The distance $x$ along the inclined plane that it will travel before again striking the slope is

A car travels first half distance with uniform speed of $60\text{km/hr}$. What should be its uniform speed (in $\text{km/hr}$) for the second half of the distance so that its average speed over the entire journey becomes $90\text{km/hr}$.

Rocky made $12\text{kg}$ of trail mix for his family's hiking trip. His family ate $8600\text{g}$ of the trail mix on the hiking trip. How many grams of trail mix did Rocky have left?

A particle moves according to the equation $x=2t^2-5t+6$ where, $x$ is in $\text{m}$. Find

$\left(i\right)$ average velocity in the first $3\text{s}$, and

$\left(ii\right)$ instantaneous velocity at $t=3\text{s}$.

A wire is $4\text{m}$ long and has a mass of $0.2\text{kg}$. The wire is kept horizontally. A transverse pulse is generated by plucking one end of the taut (tight) wire. The pulse makes four trips back and forth along the

cord in $0.8\text{sec}$. The tension is the cord will be

The binding energies per nucleon of deuteron $\left({}_1{H}^2\right)$ and helium atom $\left({}_{2}H{e}^4\right)$ are $1.1\text{MeV}$ and $7\text{MeV}$. If two deuteron atoms react to form a single helium atom, then the energy released is

A ring of mass $m$ and radius $r$ is allowed to roll down without slipping on an inclined plane having inclination ${\sin }^{-1}\left(\frac{1}{10}\right)$ from the horizontal. The magnitude of acceleration of its centre of mass is

Two beams of light having intensities $I$ and $4I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi }{2}$ at point $A$ and $2\pi$ at point $B$. Then the difference between the resultant intensities at $B$ and $A$ will be

Two particles having mass ratio $n:1$ are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is :

Ratio of minimum kinetic energies of two projectiles of same mass is $4:1$. The ratio of the maximum height attained by them is also $4:1$. The ratio of their ranges would be

The displacement of a particle varies with time as $x=12\sin \omega t-16{\sin }^3\omega t\left(\text{in cm}\right)$. If the particle is executing S.H.M, then its maximum acceleration is

If $T$ is the surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter $D$ to a diameter $2D$ is

A particle is acted by a force F = kx, where k is a positive constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

A wire of ${10}^{-3}c{m}^2$ cross sectional area carries a current of 0.25 A, then current density is

A hollow sphere rolls without slipping on the horizontal surface such that its translational velocity is $v$. Find that the maximum height attained by it on an inclined surface as shown in the figure.

The force $F_1$ that is necessary to move a body up an inclined plane is double the force $F_2$ that is necessary to just prevent it from sliding down, then: ( Given that $\varphi$ is angle of repose, $\theta$ is angle of inclined plane and $\text{w}$ is weight of the body)

Two masses $m_1$ and $m_2$ placed at a distance 'l' apart, let the centre of mass of this system be at a point named C. If $m_1$ is displaced by $l_1$ towards C and $m_2$ is displaced by $l_2$ away from C, find the distance from C where the new centre of mass will be located.

A uniform chain of length l and mass m overhangs a smooth table with its two third part lying on the table. The kinetic energy of the chain as it completely slips off the table is

The freezing point on a thermometer is marked as ${20}^{\circ }$ and the boiling point at as ${150}^{\circ }$. A temperature of ${60}^{\circ }$C on this thermometer will be read as

A particle executes simple harmonic motion (amplitude $=A$) between $x=-A$ and $x=+A$. The time taken for it to go from $0$ to $\frac{A}{2}$ is $T_1$ and to go from $\frac{A}{2}$ to $A$ is $T_2$ . Then

Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum.They use different lenghts of the pendulum and record time for different number of oscillations.The observations are shown in the table.Least count for length = 0.1cm, Least count for time = 0.1s

$\begin{array}{ccccc}\text{Student}& \text{Length of the pendulum(cm)}& \text{Number of oscillations(n)}& \text{Total time for (n) oscillation(s)}& \text{Time period(s)}\\ \text{I}& 64.0& 8& 128.0& 16.0\\ \text{II}& 64.0& 4& 64.0& 16.0\\ \text{III}& 20.0& 4& 36.0& 9.0\end{array}$

If $E_I$, $E_{II}$ and $E_{III}$ are the percentage errors in g, i.e. $(\frac{△g}{g}\times 100)$ for student I, II and III, respectively, t = $2\pi \sqrt{\frac{l}{g}}$ , then

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5\text{m/s}$. What is the height of the plane of circle from vertex of the funnel? (take $g=10{m/s}^2$)

A charge particle enters normally inside an external uniform magnetic field region of width d as shown. The magnitude of magnetic field is B. Time after which it comes out of this magnetic field will be



एक आवेश कण दर्शाए अनुसार d चौड़ाई के एक बाह्य एकसमान चुम्बकीय क्षेत्र के अन्दर लम्बवत् रूप से प्रवेश करता है। चुम्बकीय क्षेत्र का परिमाण B है। तब यह कितने समय के बाद इस चुम्बकीय क्षेत्र से बाहर आएगा?