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Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $\left(\frac{40}{3\pi }\right)\times {10}^{6}N/m^2$. If $g=10m{s}^{-2}$, then what should be the minimum radius of the wire used if it is not to break?

A solid uniform disc of mass m rolls without slipping down an inclined plane with an acceleration a. The frictional force on the disc due to surface of the plane is

Initially the nucleus of radium – 226 is at rest. It decays due to which and a particle and the nucleus of radon are created. The released energy during the decay is 4.87 Mev, which appears as the kinetic energy of the two resulted particles. $[m_{\alpha }=4.002amu,m_{Rn}=222.017amu]$

Kinetic energies of particle & radon nucleus are respectively

When a body moves in a circular path, no work is done by the force since,

A ray of light travelling in the direction $\frac{1}{2}(i+\sqrt{3}j)$ is incident on a plane mirror in the x-z plane. After reflection, it travels along the direction $\frac{1}{2}(i-\sqrt{3}j)$. The angle of incidence is:

A tuning fork of unknown frequency makes 5 beats per second with another tuning fork which can cause a closed organ pipe of length 40 cm to vibrate in its fundamental mode. The beat frequency decreases when the first tuning fork is slightly loaded with wax. Find its original frequency. The speed of sound in air is 320 m/s.

A fan is running at $300\text{rpm}$. It is switched off. It comes to rest by uniformly decreasing its angular speed in $10$ seconds. The total number of revolutions in this period are :-

The maximum wavelength of radiation that can produce photoelectric effect in a certain metal is $200nm$. The maximum kinetic energy acquired by electron due to radiation of $100nm$ wavelength will be

A particle is projected at an angle of ${30}^{\circ }$ w.r.t horizontal with speed $20m/s.$ Take the point of projection as the origin of the coordinate axes and find the angle between velocity vector and position at $t=1s$

Three partricles $A,B$ and $C$ of different masses $1\text{kg},2\text{kg}$ and $3\text{kg}$ are moving with different velocities $v_A=\hat{i}+2\hat{j},v_B=2\hat{i}+4\hat{j}$ and $v_C=3\hat{j}$. At time $t$, particles $A,B$ & $C$ are at points $(2,3),(3,2)$ & $(1,4)$ respectively. The total angular momentum of the system of $3$ particles about the origin [in ${\text{kg m}}^2\text{/s}$] is

If velocity of a particle is $v\left(t\right)=(4t+6)\text{m/s}$, the magnitude of average velocity of the particle in $10\text{sec}$ is

A rod AB of weight $W_2$ is placed over a sphere of weight $W_1$ as shown in figure. If friction is absent, the number of forces to be shown on the sphere in its $FBD$ is/are?

If length of a wire increases by $0.1\%$ due to stretching, the percentage increase in its resistance will be (Assume cross sectional area as constant)

A point object is kept in air at $40\text{cm}$ in front of an equiconvex lens silvered on one side. Radius of curvature of each side of lens is $20\text{cm}$ and refractive index of lens material is $3/2$. Where is the final image formed from silvered lens?

A coil of wire has an area of 2.0x10^-4 m², consists of 100 loops or turns, and contains a current of 0.045 A. The coil is placed in a uniform magnetic field of magnitude 0.15 T. Determine the magnetic moment of the coil.

A planet moves around sun in nearly circular orbit period of revolution 't', radius of orbit r mass of sun m.

Time period if direcyly proportional to mass of sun, distance between planet and sun and universal gravitational constant.

Prove T^{​​​​​​2} is directly proportional to r^{​​​​​​3}

The moon is observed from two diametrically opposite points A and B on earth.The angle Q substended at the moon by the two directions of observation is 1°54'.Given the diameter of the to be about 1.276×10^7m,compute the distance of the moon from the earth.

When a current of 0.5 A is passed through two resistor in series, the potential difference between the ends of series arrangment is 12.5V.on connecting them in parallel and passing a current of 1.5A ,the potential difference between their ends is TV . Calculate the two resistances.

A rectangular metal plate has dimensions of $10\text{cm}\times 20\text{cm}$. A thin film of oil separates the plate from a fixed horizontal surface. The separation between the lower surface of the rectangular plate and the upper portion of the horizontal surface is $0.2\text{mm}$. An ideal string is attached to the plate and passes over an ideal pulley to a mass $m$. When $m=125\text{gm}$, the metal plate moves at a constant speed of $5\text{cm/s}$ across the horizontal surface. Then, the coefficient of viscosity of oil in ${\text{dyne-s/cm}}^2$ is $(\text{Use}g=1000{\text{cm/s}}^2)$

In the pulley arrangement shown, the pulley $P_2$ is movable. Assuming coefficient of friction between $m$ and surface to be $\mu$, the minimum value of $M$ for which $m$ is at rest is

If the sign in equation F=-kx is changed what would happen to the motion of the oscillating body?

_ A D A C B _ _ B D C C 2 6 _ _ 2 4 8 4_ _ _ _ a _ _ b _ _ c d ? ? ? ?

A source of sound S is travelling at $\frac{100}{3}m/s$ along a road, towards a point A. When the source is 3 m away from A, a person standing at a point O on a road perpendicular to AS hears a sound of frequency v’. The distance of O from A at that time is 4m. If the original frequency is 640 Hz, then the value of v’ is (velocity of sound is 340 m/s)

The angle which a vector $\hat{i}-\hat{j}+\sqrt{2}\hat{k}$ makes with y - axis is

Two containers of sand are arranged like the block as shown in figure. The containers alone have negligible mass; the sand in these containers has a total mass $M_{tot}$; the sand in the hanging container $H$ has mass $m$.
To measure the magnitude of the acceleration of the system, a large number of experiments have been carried out where $m$ varies from experiment to experiment but $M_{tot}$ does not; that is, sand is shifted between the containers before each trial.


Which of the curves gives the tension in the connecting cord (the vertical axis is for tension)?

In a particular system, the unit of length, mass and time are chosen to be $10\text{cm}$,$10\text{gm}$ and $0.1\text{s}$ respectively. The unit of force in this system will be equivalent to

A uniform wire of length $L=1\text{m}$ is bent into the shape $V$ as shown in figure. The distance of its centre of mass from the vertex $A$ is

A body starting from rest moving with uniform acceleration has a displacement of $16\text{m}$ in first $4\text{s}$ and $9\text{m}$ in first $3\text{s}$. the acceleration of the body is

If the arcs of the same lengths in two circles subtend angles ${65}^o$ and ${110}^o$ at the center, find the ratio of their radii.

A ball strikes a wall with a velocity $\overrightarrow{u}$ at an angle $\theta$ with the normal to the wall surface and rebounds from it at an angle $\beta$ with the surface. Then:

A $100\text{m}$ long train crosses a man travelling at $5\text{km/h}$ in opposite direction in $7.2\text{s}$. Then the velocity of the train is

When a proton is released from rest in a room, it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$, it moves with an initial acceleration $3a_0$ towards west. Find the electric field and the minimum possible magnetic field in the room.

The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be

A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes up to 2 m height further, find the magnitude of the force, applied by the hand. Consider g = 10 m/$s^2$

Force F is gradually increased from zero. Determine whether the block will first slide or lift up?

Two trucks of mass M each are moving in opposite direction on adjacent parallel tracks with same velocity u. One is carrying potatoes and other is carrying onions, bag of potatoes has a mass $m_1$ and bag of onions has a mass $m_2$ (included in the mass of truck M). When trucks get close to each other while passing, the drivers exchange a bag with the other one by throwing the other one. Find the final velocities of the trucks after exchange of the bags.

The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity $\sqrt{10gl}$ whom l is the length of the pendulum. Find the tension in the string when

(a) the string is horizontal

(b) the bob is at its highest point and

(c) the string makes an angle of ${60}^{\circ }$ with the upward vertical.

A bullet travelling a velocity of 16$\frac{m}{s}$ penetrates a tree trunk and comes to rest in 0.4 m. Find the time taken during the retardation.

ILLUSTRATION: A particle (a mud pallet, say)of mass m strikes a smooth stationary wedge of mass $M$

with a velocity $v_0$, at an angle $\theta$ with horizontal. If the collision is perfectly inelastic, find the velocity of

the wedge just after the collision.

Eddy currents are produced when [CBSE PMT 1993; AFMC 2002]