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A helium nucleus makes a full rotaion in a circle of radius $0.8\text{m}$ in two seconds. The value of the magnetic field $B$ at the centre of the circle will be

An X-ray tube operates at 20 kV. A particular electron loses 5% of its kinetic energy to emit an X-ray photon at the first collision. What is the wavelength corresponding to this photon? Given that Planck's constant $=4.14\times {10}^{-15}eVs$.

A proton with kinetic energy, K strikes another proton at rest. If the collision is head – on, find the correct graph between K and the distance of closest approach, r.

A photosensitive metallic surface has work function $h{\nu }_0.$ If photons of energy $2h{\nu }_0$ fall on this surface, the electrons come out with a maximum velocity of $4\times {10}^6{\text{ms}}^{-1}.$ When the photon energy is increased to $5h{\nu }_0$, then maximum velocity of photoelectrons will be

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A body moves from A to B in 3 sec. What is its average velocity w.r.t. the origin?

Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel?

The figure shows a conducting loop being pulled out of a uniform magnetic field with a constant speed $v$. Which of the four plots, shown in the figure, may represent the power delivered by the pulling agent as a function of the constant speed $v$.

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are $0.1{\text{kg.m}}^2\text{and}10{\text{rad s}}^{–1}$ respectively while those for the second one are $0.2{\text{kg m}}^2\text{and}5{\text{rad s}}^{–1}$ respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is

A body of mass $m$ is attached to the lower and of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released, it oscillates with a time period of $3\text{s}$. When the mass $m$ is increased by $1\text{kg}$, the time period of oscillations becomes $5\text{s}$. The value of $m$ in $\text{kg}$ is

A
uniformly charged conducting sphere of 2.4 m diameter has a surface
charge density of 80.0 μC/m².
(a) Find the charge on the sphere. (b) What is the total electric
flux leaving the surface of the sphere?

Two wires of the same material (Young's modulus $Y$) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is

If $u_1$ and $u_2$ are the units selected in two systems of measurement and $n_1$ and $n_2$ are their numerical values respectively, then for constant physical quantity

You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why? Define mass. Is it scalar or vector quantity?

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A particle starts S.H.M. from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of the maximum speed, its displacement y is

[Haryana CEE 1996; CBSE PMT 1996; MH CET 2002]

A short bar magnet is moved with constant velocity along the axis of a short coil. The magnet enters into the coil and then leaves it. The variation of induced emf $\left(\epsilon \right)$ with time $\left(t\right)$ is best represented as

The extension in a string obeying Hooke's law is x. The speed of a transverse wave in a stretched string is v. If the extension in the string is increased to 1.5x, the speed of the wave will be

Resistor $R_2$ in fig. is to limit the emf that develops across the inductor when the switch is opened. What can be its value so that the inductor emf does not exceed $100\text{V}$? Assume that before opening, the circuit is in steady state.

A particle slides along a track with elevated ends and a flat central part, as shown in figure. The flat portion $BC$ has a length $l=3.0\text{m}$. The curved portions of the track are frictionless. For the flat part of the track the coefficient of kinetic friction is ${\mu }_k=0.20$, If the particle is released at point $A$ which is at height $h=1.5\text{m}$ above the flat part of the track, then Where does the particle finally comes to rest w.r.t $B$ ?

The pitch of a screw gauge is $1\text{mm}$ and there are $100$ divisions on circular scale. When the faces $A$ and $B$ are just touching each without putting anything between the studs, the ${32}^{\text{nd}}$ division of the circular scale coincides with the reference line. The error in measurement due to screw gauge will be (zero of linear scale is not hidden from circular scale when $A$ and $B$ touches)

The pulley and block arrangement is as shown in the figure.

If string is massless and inextensible, pulley and surfaces are frictionless. Find the horizontal component of the acceleration of COM for the system of blocks. Take $g=10{\text{m/s}}^2$.

In a Carnot heat engine, the temperature of source and sink are $500\text{K}$ and $375\text{K}$ respectively. The efficiency of engine is

If $(a,b),a\ne 0$ be the point on the curve $9y^2=x^3$ where normal to the curve make equal intercepts with the axes, then the value of $(a+b)$ is :

Quick question. The smallest possible value of angular momentum for an electron in the hydrogen atom, in appropriate units, is –

Let $z$ be a complex number such that the principal value of argument, $\arg z>0$. Then $\arg z–\arg (–z)$ is

A string tied between $x=0$ and $x=2.45\text{m}$ vibrates in fundamental mode. The amplitude of vibration is $1\text{m}$, tension in the string is $9.8\text{N}$ and mass per unit length of the string is $1\text{g}$. Then, total energy of the string is

What will be the velocity of block A in the arrangement shown ?

In a system of units, the relations between velocity, acceleration and force are given by $v_2=\frac{v_1{ϵ}^2}{\tau },a_2=a_1ϵ\tau ,F_2=\frac{F_1}{ϵ\tau }$ where $ϵ$ and $\tau$ are constants. Then in this new system, (where m is mass and L is length)