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Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity v and other with a uniform acceleration a. If $\alpha$ is the angle between the lines of motion of two particles then the least value of magnitude of relative velocity will be at time given by

1. 8.18

According to Maxwell’s hypothesis, a changing electric field gives rise to

The electric field of a plane polarized electromagnetic wave in free space at time $t=0$ is given by an expression $\overrightarrow{E}(x,y)=10\hat{j}\cos \left[\right(6x+8z\left)\right]$. The magnetic field $\overrightarrow{B}(x,z,t)$ is given by



($c$ is the velocity of light)

A thin uniform rod of length $3\text{m}$ and mass $M$ is held horizontally by two vertical strings attached to the two ends, as shown in figure. One of the strings is cut. Find the angular acceleration of the rod at the moment it is cut. (Take $g=10{\text{m/s}}^2$).

A body covers $10m$ in $2^{nd}$ second and $25m$ in $5^{th}$ second of its motion. If the motion is uniformly accelerated, how far will it go in the $7^{th}$ second?

1. 1.54

A hydroelectric power station take sits water from a lake whose water level is at a height of 50 m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce a power output of 1 MW.(Take g=10 m$s^{-2}$).

In figure shown, all surfaces are smooth. A force $F=2mg$ is acting on block $A$. If $R$ is contact force between $A$ and $B$ and $a$ is acceleration of $B$, then

A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of 1$1.0\times {10}^{-2}T$ near the centre of the solenoid.

If $\overrightarrow{F}$ is a force acting on a particle having the position vector $\overrightarrow{r}$ and $\overrightarrow{\tau }$ is the torque due to this force about the origin, then-

Find the electric field at point $P$ as shown in the figure on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2}L$.

The greatest acceleration or deceleration that a train may have is 'a'. The minimum time in which the train may reach from one station to the other separated by a distance 'd' is

A current carrying square loop is placed near an infinitely long current carrying wire as shown in fig. The torque acting on the loop is

The effective resistance between points $\text{P}$ and $\text{Q}$ of the electrical circuit shown in the figure is:

Given in
Fig. 6.11 are examples of some potential energy functions in one
dimension. The total energy of the particle is indicated by a cross
on the ordinate axis. In each case, specify the regions, if any, in
which the particle cannot be found for the given energy. Also,
indicate the minimum total energy the particle must have in each
case. Think of simple physical contexts for which these potential
energy shapes are relevant.

An annular disc has inner and outer radius $R_1$​ and $R_2$​ respectively. Charge is uniformly distributed. Surface charge density is $\sigma$. Find the electric field at any point distant $y$ along the axis of the disc.

One of the lines in the emission spectrum of ${\text{Li}}^{2+}$ has the same wavelength as that of $2^{nd}$ line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is :-

Two mirrors are inclined at an angle $\theta$. For an object placed in front of them, $11$ images are noticed. Find the angle between the mirrors.

A strip of wood of mass $M$ and length $l$ is placed on a smooth horizontal surface. An insect of mass $m$ starts at one end of the strip and walks to the other end in time $t$, moving with constant speed. The speed of the insect as seen from the ground is

The velocity of a small ball of mass $M$ and density $\rho$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $\frac{\rho }{2},$ then the viscous force acting on the ball will be

Each atom of an iron bar $5cm\times 1cm\times 1cm$ has a magnetic moment $1.8\times {10}^{-23}A{m}^2$ Knowing that the density of iron is $7.78\times {10}^{3}k{g}^{-3}m,$ atomic weight is 56 and Avogadro's number is $6.02\times {10}^{23}$ the magnetic moment of bar in the state of magnetic saturation will be

Two balls are placed as shown in the figure on a weightless support formed by two smooth inclined planes each of which forms an angle of $\alpha$ with the horizontal. The support can slide without friction along a horizontal plane. The upper ball of mass $m_1$ is released. Determine the condition under which the lower ball of mass $m_2$ starts climbing up the support.

In Rutherford's $\alpha -$ particle scattering experiment, what will be the angle of scattering for an impact parameter $b=0$?

A bar magnet is tied to a string and hung from the ceiling. Gravitational force of attraction by the earth is pulling the magnet down. According to Newton's first law, the magnet should move towards ground as it is acted upon by a force. Then why isn't it happening.

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\mathring{\text{A}}$ and ${\lambda }_2=5000\mathring{\text{A}}$, the ratio of their respective resolving powers ( corresponding to ${\lambda }_1$ and ${\lambda }_2$ ) is,

A series $\text{LCR}$ circuit connected across $(200\text{V},60\text{Hz})$ source. It consists of a capacitor of capacitive reactance $30\Omega$, a non-inductive resistor of $40\Omega$ and an ideal inductor of inductive reactance $90\Omega$ as shown in the figure. The average power dissipated in the circuit is nearly







​​​​​​​$[$0.77 Mark$]$

Two rods of different materials having coefficients of thermal expansion ${\alpha }_1,{\alpha }_2$ and Young's modulii $Y_1,Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If ${\alpha }_1:{\alpha }_2=2:3$ and thermal stresses developed in the two rods are equal, then $Y_1:Y_2$ is equal to

The position of an object is x=a+bt^2 where a = 6 CM B =9 M / s Square what is the average velocity between t=2 second and t=4 second

A train weighing 1000 tons is moving on a horizontal track with a uniform velocity of $10m/s$.The total resistance to the motion of the train is 5 kgf per ton.If $g=10m/s^2$,then the power of the engine is

An object is placed symetrically between the two perpendicular plane mirrors as shown in the figure. The equation of the locus of all the images formed by this arrangement is



[Assume the intersection point of the mirrors as the origin.]