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A narrow beam of singly charged potassium ions of kinetic energy 32 ke V is injected into a region of width 1.00 cm having a magnetic field of strength 0.500 T as shown in figure (34.E16). The ions are collected at a screen 95.5 cm away from the field region. If the beam contains isotopes of atomic weights 39 and 41, find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion $=A(1.6\times {10}^{-27})$ kg where A is the mass number.

For CE transistor amplifier, the audio signal voltage across the collector resistance of $2k\Omega$ is $4V$. If the current amplification factor of the transistor is $100$ and the base resistance is $1k\Omega$, then the input signal voltage is

A force $\overrightarrow{F}=\overrightarrow{v}\times \overrightarrow{A}$ is exerted on a particle in addition to the force of gravity, where $\overrightarrow{v}$ is the velocity of the particle and $\overrightarrow{A}$ is a constant vector in the horizontal direction.With what minimum speed a particle of mass m be projected so that it continues to move undeflected with a constant velocity ?

In a charged capacitor, the energy resides as

12 cells each having same e.m.f are connected in series and are kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and two cells identical with the others. The current is 3A when the cells and the battery support each other and 2A when the cells and the battery oppose each other. The number of cells in the battery that are wrongly connected is

A point source of light is moving at a rate of 2 cm-s${}^{-1}$ towards a thin convex lens of focal length 10 cm along its optical axis. When the source is 15 cm away from the lens the image is moving at

A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity $\omega$. This can be considered as equivalent to a loop carrying a steady current $\frac{Q\omega }{2\pi }$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The applications of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $\gamma$.

The magnitude of the induced electric field in the orbit at any instant of time during the time internal of the magnetic field change is

A mass $m$ is hung on an ideal massless spring. Another equal mass is connected to the other end of the spring. The whole system is at rest. At $t=0$, $m$ is released and the system falls freely under gravity. Assume that natural length of the spring is $L_0$, its initial stretched length is $L$ and the acceleration due to gravity is $g$.
What is distance between masses as function of time ?

A person moves towards a stationary source of sound, with a velocity of one – fifth of the velocity of sound. The apparent frequency of the sound as heard by a person

If 10^14 electrons are removed from neutral metal spheres , the what is charge on the spheres

For recording, we need sound of 50 dB at 2m from a speaker. What power output is required?

A circular loop of rope of length L rotates with uniform angular velocity ω about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

An $L-$ shaped system of two identical rods of mass $m$ and length $l$ each, are resting on a peg $P$ as shown in the figure. Find the period of oscillations if the system is displaced slightly in its plane by a small angle $\theta$ ?

Can I get the notes of applications of Gauss law

A heavy particle is suspended by a 1.5 in long string. It is given a horizontal velocity of $\sqrt{57}m/s$. (a) Find the angle made by the string with the upward vertical, when it becomes slack. (b) Find the speed of the particle at this instant. (c) Find the maximum height reached by the particle over the point of suspension. Take $g=10m/s^2$.

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 spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by

If temperature of a black body increases from $7^{\circ }Cto{287}^{\circ }$ , then the rate of energy radiation increases by

A spherical body of radius $b=\frac{4}{\pi }\text{m}$ has a concentric cavity of radius $a=\frac{2}{\pi }\text{m}$ as shown. Thermal conductivity of the material is $100{\text{W/m}}^{\circ }\text{C}$. Find the thermal resistance between inner and outer surface.

Light of wavelengths $\lambda$ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance D. The linear width of the principal maximum is equal to the width of the slit if D equals

A uniform bar of length $6a$ and mass $8m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$, moving in the same horizontal plane with speeds $2v$ and $v$ respectively strike the bar (as shown in figure) and stick to the bar after collision. By denoting angular velocity (about centre of mass), total energy and velocity of centre of mass after collision as $\omega ,E$ and $v_o$ respectively, we can say that

Each of the resistances shown in figure (45-E2) has a value of $20\Omega .$ Find the equivalent resistance between A and B. Does it depend on whether the point A or B is at higher potential ?

In problems 25 to 30, assume that the resistance of each diode is zero in forward bias and is infinity in reverse bias.

At the height 80 m, an aeroplane is moving with 150 m/s. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped (given g = 10 $m/s^2$)

Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is $4.0\times {10}^{–3}kg{s}^{–1}$ , what is the pressure difference between the two ends of the tube? (Density of glycerine =$1.3\times {10}^{3}kg{m}^{–3}$ and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct].

A car starting from rest accelerates at the rate $f$ through a distance $s$, then continues at constant speed for time $t$ and then decelerates at rate $\frac{f}{2}$ to come to rest. If the total distance covered is $15s$, then which one is correct?

A polythene piece rubbed with wool is found to have a negative charge of $3\times {10}^{–7}$ C. Estimate the number of electrons transferred (from which to which?) Is there a transfer of mass from wool to polythene?

The figure shows a man standing stationary with respect to a horizontal conveyor belt. If the coefficient of static friction between the man's shoes and the belt is $0.2$, upto what acceleration of the belt can the man continue to be stationary relative to the belt? Mass of the man $=65\text{kg}$. ($g=10{\text{m/s}}^2$)

Which of following rotational physical quantities do not match to given translational analogies?

How can a string of length $l$ be made into a rectangle so as to maximize the area of the rectangle?

A steel ball having mass $100\text{g}$ is moving with velocity $20\text{m/s}$. In the same direction, a ball of clay having mass $20\text{g}$ is moving with velocity $10\text{m/s}$. If after some time, both balls collide and stick together, what will be the speed of steel ball after collision?

Work function of caesium is $2.14eV$. What is the wavelength of incident light if photocurrent is brought to zero by a stopping potential of $0.6V$?

If $\overrightarrow{A}$ and $\overrightarrow{B}$ acting in such a way that they satisfy the relation,
$|\overrightarrow{A}\times \overrightarrow{B}|=\overrightarrow{A}.\overrightarrow{B}$. Then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$

The descending pulley has a radius $20\text{cm}$ and moment of inertia $0.2{\text{kg-m}}^2$, considering it to be a disc. The fixed pulley is light and the horizontal plane is frictionless. Find the acceleration of the block if its mass is $1.0\text{kg}$. Take $g=10{\text{m/s}}^2$.

What is the concept of Degree of freedom?Can you please explain in detail?

In the figure below, $10\text{mC}$ charge is fixed. A $50\mu \text{C}$ charge having mass $10\text{g}$ is projected from infinity towards the $10\text{mC}$ charge. Calculate initial velocity of projection if minimum distance between the charges is $10\text{cm}$.

In a meter bridge, the balancing length from left is found to be $20cm$ when standard resistance of $1\Omega$ is in right gap. The value of unknown resistance is

A body is projected from the top of a tower of height $32\text{m}$ with a velocity of $20\text{m/s}$ at an angle of ${37}^{\circ }$ above the horizontal. Find the velocity with which it hits the ground.

(Take $g=10m/s^2$)

Consider a ball falls from a height of 2 m and rebounds to a height of 0.5 m.If the mass of the ball is 60g, then find the impules and the average force between the ball and the ground.The time for which the ball and the ground are in contact was 0.2s