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A car moves on a circular path of radius 10 metre. It complete 5 revolution in 5 minute. What is its average speed?

An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_e,R_p,R_d$ and $R_{\alpha }$. It follows that

A planet is at an average distance $d$ from the sun and its average surface temperature is $T$. Assume that the planet receives energy only from the sun, and loses energy only through radiation from its surface. Neglect atmospheric effects. If $T\propto d^{-n}$, the value of $n$

A uniform rod of mass $5\text{kg}$ and length $3\text{m}$ is held at an angle $\theta ={37}^{\circ }$ with the horizontal as shown in the figure. The potential energy of the rod is (in $\text{J}$)

A and B are concentric circular conductors with center O and carrying currents $I_1$ and $I_2$ as shown in fig. The ratio of their radii is 1: 2 and ratio of their flux densities at O is 1:3 The value of $\frac{I_1}{I_2}$ is

Two bodies of masses $10\text{kg}$ and $2\text{kg}$ are moving with velocities $2\hat{i}-7\hat{j}+3\hat{k}$ and $-10\hat{i}+35\hat{j}-3\hat{k}\text{m/s}$ respectively. The velocity of their centre of mass is

A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is

A stunt driver of mass $60\text{kg}$ rides a bike inside a hollow metallic sphere of radius $45\text{m}$. Assume the bike moves in the central plane of the sphere. If the coefficient of static friction between the wheels of the bike and the metal surface is $0.8$, what must be the minimum speed of the driver so that he does not crash? Take $g=10{\text{m/s}}^2$.

A mass $m$ rests on a horizontal surface. The coefficient of friction between the mass and the surface is $\mu$. If the mass is pulled by a force $F$ as shown in figure, the limiting friction between mass and the surface will be

A body starts from orgin and moves along x-axis such that its velocity is $v=(4t^3-2t)$ m/s. Acceleration of particle when it is 2 m from origin is.

A barometer tube reads $76\text{cm}$ of $\text{Hg}$. If the tube is gradually inclined at an angle of ${30}^{\circ }$ with horizontal, then find the length of the mercury column in the barometer tube.

The two nearest harmonics of a tube closed at one end and open at the other end are $220\text{Hz}$ and $260\text{Hz}$. What is the fundamental frequency of the system?

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure. Assume that the pulleys are frictionless and string is inextensible.

Find the effective capacitance of the following system.

A concave mirror is placed at the bottom of an empty tank with face upwards

and axis vertical. When sunlight falls normally on the mirror, it is

focussed at distance of 32 cm from the mirror. If the tank filled with water

upto a height of 20 cm, then the sunlight will now get focussed at

[UPSEAT 2002]

An object placed in front of a concave mirror of focal length $0.15\text{m}$ produces a virtual image which is twice the size of the object. The position of the object from the mirror as per sign convention is

A solid sphere of mass $5\text{kg}$ and radius $1\text{m}$ is kept on a rough surface. A force $F=30\text{N}$ is acting at the top most point. Friction required for pure rolling is

An object of mass $M$ is kept on a rough table as seen from above. Forces are applied as shown. Find the direction (from the vertical) of static friction if the object does not move.

An ideal gas is taken through a cyclic thermodynamic process through four steps. The amount of heat exchanged in the steps are $Q_1=+5960\text{J},Q_2=-5600\text{J},Q_3=-3000\text{J},Q_4=+3600\text{J}$ respectively. The corresponding quantities of internal energy changes are $\Delta U_1=+3760\text{J},\Delta U_2=-4800\text{J},\Delta U_3=-1800\text{J}$ and $\Delta U_4$. Find the value of $\Delta U_4$ and work done during the cyclic process.

In a double star system of two stars of masses m and 2m, rotating about their centre of mass. Their time period of rotation about their centre of mass will be proportional to

A long cylinderical magnet is moving at a constant velocity $v$ towards a circular wire ring whose radius is slightly larger than that of magnet and passes through it. Graph of flux vs time can be.

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

The length of the wire shown in figure between the pulley and fixed support is $1.5\text{m}$ and mass is $12.0\text{g}$. The frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulley and the fixed support, is: [Assume the pulley acts as a fixed support and consider $g=10{\text{m/s}}^2$]

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

A particle is aimed at a mark which is in the same horizontal plane as that of the point of projection. It falls $10m$ short of the target when it is projected with an elevation of ${75}^{\circ }$ and falls $10m$ ahead of the target when it is projected with an elevation of ${45}^{\circ }$. If $\theta$ is the correct elevation so that it exactly hits the target, find the value of $\sin 2\theta$ (for the same velocity of projection)

A particle of mass $1\text{kg}$ is initially at rest. A force starts acting on it in one direction whose magnitude changes with time. The (F - t) graph is shown in figure. The velocity of the particle at the end of $10\text{s}$ is

A curve has a radius of $50\text{metres}$ and a banking angle of ${15}^{\circ }$. What is the critical speed (the speed for which no friction is required between the car's tyres and the surface) for a car to travel safely on this curve ? Take $g=10{\text{m/s}}^2$.

A square is made by joining four rods each of mass $m$ and length $L$ each. Its moment of inertia about an axis $PQ,$ on its plane and passing through one of its corners (as shown in the figure) will be:

Which of these light sources will have a cylindrical wave front?

A block of mass 30.0 kg is being brought down by a chain. If the block acquires a speed of 40.0 $\frac{cm}{s}$ in dropping down 2.00 m, find the work done by the chain during the process.

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?

Find charge on $12nF$ which is in direct contact to battery (initially all capacitors are uncharged)

One mole of an ideal monatomic gas is taken along the process in which $P{V}^x=\text{constant}$. The graph shown represents the variation of molar heat capacity of such a gas with respect to $x$ . Find the values of $C^{\prime }$ and $x^{\prime }$ indicated in the diagram.

At a distance of $10\text{m}$ from a point source, loudness is found to be $20\text{dB}$. The distance from the source where loudness is $0\text{dB}$ is

Projection of $\overrightarrow{A}=\hat{i}-\hat{j}$ along $\overrightarrow{B}=\hat{k}$ is

A sphere of radius $R$ and density ${\rho }_1$ is dropped in a liquid of density $\sigma$. Its terminal velocity is $v_1$ . If another sphere of radius $R$ and density ${\rho }_2$ is dropped in the same liquid, its terminal velocity will be:

The displacement of tip of the second hand of an analog watch when it turns for $15\text{sec}$ is

In the arrangement shown in the figure, $m_A=1\text{kg},m_B=4\text{kg}$. String is light and inextensible while pulley is smooth. Coefficient of friction between the block $A$ and the table is $\mu =0.2$. Find the speed of both the blocks when block $B$ has descended by a height $h=1\text{m}$. ( Take $g=10{\text{m/s}}^2$).

A cubical block is moving on a horizontal smooth plane. It hits a ridge at point $\text{O}$. The angular speed of the block after it hits $\text{O}$ is

A railway carriage box has its geometric centre (i.e we will assume the force due to gravity to act at this point) at a height of $1\text{m}$ above the rails, which are $1.5\text{m}$ apart. The maximum safe speed at which it could travel round an unbanked curve of radius $100\text{m}$ is

Two equal drops of water are falling through air with a steady velocity $v$. If the drops coalesce, the new velocity will be

How long will the ball take to come back to the point from where it was thrown?

An insulating rod of length $l$ carries a charge $q$ distributed uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency $f$ about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is

A monoatomic gas undergoes an adiabatic process as indicated in the given figure. Find the work done during the process.

In a game house the above punch bag has the shown set up. If you punch the bag at mean position and it gets compressed by a distance x m, then it will come back to mean and get elongated by the same distance x m. Rohit punches the bag and compresses it by 5 cm. What is the magnitude of maximum displacement (M) and magnitude of minimum displacement (m)?

Starting from rest, a fan takes four seconds to attain the maximum speed of $800\text{rpm}$ (revolutions per minute). Assuming uniform acceleration, calculate the time taken by the fan in attaining half the maximum speed.