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Vector $A$ having magnitude $\sqrt{2}$ units makes an angle ${45}^{\circ }$ with horizontal and vector $B$ having magnitude $2$ units makes an angle ${30}^{\circ }$ with horizontal as shown in the figure. What is $\overrightarrow{A}-\overrightarrow{B}$?

When water droplets merge to form a bigger drop?

Consider a block of conducting material of resistivity $\rho$ shown in the figure. Current l enters A and B leaves from D. We apply superposition principle to find voltage $\Delta V$ developed between B and C. The calculation is done in the following steps:
(a) Take current l entering from A and assume it to spread over a hemispherical surface in the block.
(b) Calculate field E(r) at distance r from A by using Ohm’s law $E=\rho j$, where j is the current per unit area at r.
(c) From the r dependence of E(r), obtain the potential V(r) at r.
(d) Repeat (i), (ii) and (iii) for current l leaving D superpose results for A to D.

For current at A, the electric field at a distance ‘r’ from A is

In a Young's double slit experiment, $d=1\text{mm},\lambda =6000\mathring{\text{A}}$ and $D=1\text{m}$. The two slits have equal intensity. The minimum distance between two points on the screen, having $75\%$ intensity of the maximum intensity is,

Two S.H.M's of unequal amplitude with same frequency (act) on a particle at right angle, with a phase difference of $\frac{\pi }{2}$. The resultant motion is:

Solve the previous problem if the friction coefficient between the 2.0 kg block and the plane below it is 0.5 and the plane below the 4.0 kg block is frictionless.

A long solenoid has 200 turns per cm and carries a current of 2.5 amps. The magnetic field at its centre is (${\mu }_0=4\pi \times {10}^{-7}weber/amp-m$)

A ball of mass $m$ is suspended by a massless string of length $l=10\text{m}$ from a fixed point as shown in the figure below. A ball of mass $2m$ strikes at an angle $\theta ={45}^{\circ }$ from the horizontal and sticks to it. If the system deflects by angle $\varphi =\frac{\pi }{2}$, then the velocity of the system just after the collision and the velocity of $2m$ particle before collision are, respectively $\left(\text{in m/s}\right)$

Three positive charges of equal magnitude $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as

A straight wire of length $l$ is bent into a $\left(i\right)$ a circular loop $\left(ii\right)$ a square loop, and each having single turn. ${\text{M}}_C$ and ${\text{M}}_S$ indicate their dipole moments respectively. If the loops carry the same current, the value of $\frac{{\text{M}}_C}{{\text{M}}_S}$ is:

An infinite number of identical capacitors, each of capacitance $1\mu \text{F}$ are connected as in the figure below. Find the equivalent capacitance between $\text{A}$ and $\text{B}$ is

If $y=2si{n}^2\theta +tan\theta$, then $\frac{dy}{d\theta }$ will be

What is the minimum eneregy required to launch a satellite of mass $m$ from the surface of earth of radius $R$ in a circular orbit at an altitude of $2R$ from surface of earth?

Question 14

The path of a ray of light coming from air passing through a rectangular glass slab traced by four students are shown as A, B, C and D in figure. Which one of them is correct?







(a) A

(b) B

(c) C

(d) D

A rod is inserted as the core in the current-carrying solenoid of the previous problem. (a) What is the magnetic intensity H at the centre ? (b) If the magnetization I of the core is found to be 0.12 A $m^{-1}$ find the susceptibility of the material of the rod. (c) Is the material paramagnetic, diamagnetic or ferromagnetic ?

In a meter bridge experiment, the value of unknown resistance is 2$\Omega$. To get the balancing point at $40$ $\text{cm}$ distance from the same end, then what will be the resistance in the resistance box?

The transparent media of refractive indices 1.2, $n$, $n^{{}^{\prime }}$ respectively, are stacked as shown. A ray of light follows the path shown. Then,

The root mean square velocity of the molecules in a sample of helium is $\frac{5}{7}th$ that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is 0°C, then the temperature of the helium sample is about

A tuning fork with the time period of $\frac{1}{256}\text{s}$ produces a sound wave which has separation between adjacent compression and rarefaction of $0.7\text{m}$. Then, the speed of sound is

Two putty balls of equal masses moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of $45\sqrt{2}m{s}^{-1}$ each, the velocity of their combined mass after collision is

A particle is projected at time t = 0 from a point P with a speed $v_0$ at an angle of ${45}^{\circ }$ to the horizontal. Find the magnitude and the direction of the angular momentum of the particle about the point P at time $t=\frac{v_0}{g}$

Three light strings are connected at the point $P$. A weight $W$ is suspended from one of the strings. End $A$ of string $AP$ and end $B$ of string $PB$ are fixed as shown. In equilibrium, $PB$ is horizontal and $PA$ makes an angle of ${60}^{\circ }$ with the horizontal. If the tension in $PB$ is $30N$, then the tension in $PA$ and weight $W$ are respectively given by

What is the capacitance of a parallel plate capacitor having $40\text{cm}\times 40\text{cm}$ square plates separated by the distance $10\text{cm}$?

(Take ${ϵ}_o=8.85\times {10}^{-12}\text{F/m}$)

The width of man's face is $D$. The distance between the eyes of the man is $d$. Then the minimum width of plane mirror to see his full face is

Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be maximum work function of the metal ?

In Young's double slit experiment, the distance $d$ between the slits $S_1$ and $S_2$ is $0.1\text{mm}$. What should be the maximum width of each slit, so as to obtain ${10}^{th}$ maxima of the double slit pattern within the central maximum of the single slit pattern?

Work done when a force $\overrightarrow{F}=(\hat{i}+2\hat{j}+3\hat{k})\text{N}$ acting on a particle displaces it from the point $r_1=(\hat{i}+\hat{j}+\hat{k})$ to the point $r_2=(\hat{i}-\hat{j}+2\hat{k})$ is