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A molecule of a gas, filled in a discharge tube, gets ionized when an electron is detached from it. An electric field of $5.0kV{m}^{-1}$ exists in the vicinity of the event (a) Find the distance travelled by the free electron in 1 \mu s assuming no collision. (b) If the mean free path of the electron is 1.0 mm, estimate the time fo transit of the free electron between successie collision.

A circular loop of radius a, carrying a current i, is placed in a two - dimensional magnetic field. the centre of the loop coincides with the centre of the field (figure 34 - E4). The strength of the magnetic field at the periphery of the loop is B. Find the magnetic force on the wire.

The temperature reading of a bath on Celsius and Fahrenheit thermometers are in the ratio $2:5$. The temperature of the bath is

A body is projected from the ground with an upward velocity of $100\text{m/s}$. The body explodes into two fragments of mass $m$ and $2m$ just after it was projected. If the lighter part comes to rest instantly, find the maximum height attained by the other part.[Take $g=10{\text{m/s}}^2$]

A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is

A small ball of density $\rho$ is immersed in a liquid of density $\sigma (>\rho )$ to a depth h and released. The height above the surface of water up to which the ball will jump is

Aliens on the planet Xargon spot a distant dying star, 5 light years far. If we see the star dying today then after how much time will the star's explosion be heard by the Xargonians? (Assume Xargonians to be an immortal peace loving race) speed of sound $3\times {10}^2$ m/s

A long solenoid of radius 2 cm has 100 turns/cm and carries a current of 5 A. A coil of radius 1 cm having 100 turns and a total resistance of $20\omega$ is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.

A boy of mass $45\text{kg}$, whose leg bones have a cross-sectional area of $5{\text{cm}}^2$ and length $50\text{cm}$, falls through a height of $2\text{m}$ without breaking his leg bones. If the bones can withstand a stress of $0.9\times {10}^8{\text{Nm}}^{-2}$, calculate the Young's modulus for the material of the bone. Use, $g=10{\text{ms}}^{-2}$

A particle starts with an initial velocity $2.5\text{m/s}$ along the positive $x-$ direction and it accelerates uniformly at the rate $0.50{\text{m/s}}^2$. The distance travelled by the particle in first two seconds will be

The magnification in a spherical mirror is:

In the figure given the position-time graph of a particle of mass $0.1\text{kg}$ is shown. The impulse at $t=2\text{s}$ is :

A train has to negotiate a curve of radius $2000\text{m}$. By how much should be the outer rail be raised with respect to the inner rail for a safe travelling speed of $72{\text{kmh}}^{-1}$?

The distance between the rails is $1\text{m}$.

$($Take $g=10{\text{m/s}}^2)$

The length of an elastic string is $a$ metre when the tension is $4\text{N}$ and $b$ metre when the tension is $5\text{N}$. The length in metre, when the tension is $9\text{N}$ is

The ratio between rms velocity of $H_{2}and{O}_2$ at 800 K is

A massless platform is kept on a light elastic spring as shown in fig. When a particle of mass 0.1 kg is dropped on the pan from a height of 0.24 m, the particle strikes the pan, and the spring is compressed by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m?

In the figure shown below, $m_a=3\text{kg}$ and $m_b=1\text{kg}$. String is inextensible and light. Find the acceleration of centre of mass of the system.

An inductor coil, a capacitor and an AC source of $24\text{V}\left(rms\right)$ are connected in series. When the frequency of the source is varied, a maximum rms current of $6\text{A}$ is observed. If the inductor coil is connected to a DC battery of emf $12\text{V}$ and internal resistance $4\Omega$, what will be steady state current through the battery.

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $–\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in (figures are schematic and not drawn to scale)

There is a rectangular metal plate in which two cavities in the shape of a rectangle and a circle are made, as show with dimensions. $P$ and $Q$ are centers of these cavities. On heating the plate, which of the following quantities increase?

What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line

A person wants to drive on the vertical surface of a large cylindrical wooden 'well' commonly known as death well' in a circus. The radius of the well is R and the coefficient of friction between the tyres of the motorcycle and the wall of the well is ${\mu }_s$. The minimum speed, the motorcycle must have in order to prevent slipping, should be

A body of mass m moving with a velocity v in the x-direction collides and sticks with another body of mass M moving with a velocity V in the y-direction. The magnitude of the momentum of the composite body is

A constant force of $10\text{N}$ applied on the flywheel of radius $20\text{cm}$ as shown in figure. If the flywheel covers an angular displacement of ${60}^{\circ }$. Calculate the work done on the flywheel.
(Assume $\pi =3$)

A long straight wire is parallel to one edge as shown in figure. If the current in the long wire varies in time as $i=I_0{e}^{-t/\tau }$, what will be the induced emf in the loop ?

When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sinr is as shown in the graph. From this, one can conclude that

Where should the tank be punctured so that water coming out has maximum horizontal range?

A glass flask is filled up to a mark with 50 cc of mercury at ${18}^{\circ }C$ . If the flask and contents are heated to ${38}^{\circ }C$ , how much mercury will be above the mark ? (coefficient of linear expansion for glass is 9 × ${10}^{-6}{/}^{\circ }C$ and coefficient of real expansion of mercury is 180 × ${10}^{-6}{/}^{\circ }C$)

A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is