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Two charges $3\times {10}^{-8}$ and $2\times {10}^{-8}$ are located 15 cm apart.At what point on the line joining the two charges is the electric potential zero? Take potential at infinity to be zero.

A straight wire is bent in a shape shown in the diagram. It carries a steady current $I$. The magnetic field at the Center $O$ of the arcs will be,

1. 341

Suppose the charge of a proton and an electron differ slightly. One of them is $-e$, the other is $(e+\Delta e)$. If the resultant of electrostatic force and gravitational force between two hydrogen atoms placed at a distance $d$ (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of [Given mass of hydrogen $m_h=1.67\times {10}^{-27}kg$]

Four positive charges $(2\sqrt{2}-1)Q$ are arranged at the four corners of a square. Another charge $q$ is placed at the centre of the square. For what value of $q$ , is the resulting force acting on each corner charge be zero ?

The electric force on a charge $q_1$ due to $q_2$ is $(4\hat{i}-3\hat{j})\text{N}$. The unit vector in the direction of electirc force on $q_2$ due to $q_1$ will be:

1. 0.5

What is the maximum number of components, a vector can have in different planes?

Read each statement
below carefully and state with reasons and examples, if it is true or
false;

A particle in
one-dimensional motion

(a) with zero speed at
an instant may have non-zero acceleration at that instant

(b) with zero speed may
have non-zero velocity,

(c) with constant speed
must have zero acceleration,

(d) with positive value
of acceleration mustbe speeding up.

Each atom of an iron bar of size$(5\text{cm}\times 1\text{cm}\times 1\text{cm})$ has a magnetic moment $1.8\times {10}^{-23}{\text{Am}}^2$. What will be the magnetic moment of the bar in the state of magnetic saturation?

$[{\rho }_{\text{iron}}=7.8\times {10}^3{\text{kgm}}^{-3},A_{\text{atomic weight}}=56]$

$[N_{\text{Avogadros Number}}=6.02\times {10}^{23}{\text{mol}}^{-1}]$

A potentiometer wire $\text{AB}$ is $100\text{cm}$ long and has a total resistance of $10\Omega$. if the galvanometer shows zero deflection at the position $\text{C}$, then find the value of unknown resistance $\text{R}$.

A compound microscope has an eye piece of focal length $10\text{cm}$ and an objective of focal length $4\text{cm}.$ Calculate the magnification, if an object is kept at a distance of $5\text{cm}$ from the objective so that final image is formed at the least distance vision $\left(20\text{cm}\right)$.

1. 3

Which of the following sets of concurrent forces may be in equilibrium

A hollow metallic sphere of radius $20\text{cm}$ surrounds a concentric metallic sphere of radius $5\text{cm}$. The space between the spheres is filled with a material of thermal conductivity $k$. The inner and outer spheres are maintained at ${50}^{\circ }\text{C}$ and ${10}^{\circ }\text{C}$ respectively and it is found that $100\text{J}$ of heat passes from the inner to the outer surface per second. Find the value of $k$.

A particle of mass $5\text{kg}$ is projected vertically upwards from point $D$ on the ground. The ratio of potential energy at point $B$ and at point $A$ is (take point D as reference)

A cylinder weighing $‘W^{\prime }$ is resting on a V-groove as shown in figure. How many forces should be shown in the $FBD$?

The surface energy of a liquid drop is u. It is splitted into 103 equal droplets. Then its surface energy becomes:

A current carrying wire heats a metal rod. The wire provides a constant power $\left(P\right)$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature ($T$) in the metal rod changes with time ($t$) as $T\left(t\right)=T_0(1+\beta t^{\frac{1}{4}})$, where $\beta$ is a constant with appropriate dimension while $T_0$ is a constant with dimension of temperature. The heat capacity of the metal is

Which of these statements is/are true about internal energy (Eint) of a system of gas?

A hypothetical butterfly net is in a uniform electric field of magnitude $E=3.0\hat{i}{\text{mNC}}^{-1}$. The circular rim of radius $R=11\text{cm}$, is aligned perpendicular to the field as shown in the diagram. If the butterfly net contains no net charge then find the magnitude of electric flux $(|\varphi |)$ passing through the circular rim of net.

Question 2

(i) What is the chemical name of the polymers that make up cotton?

A parallel plate capacitor has $1\mu \text{F}$ capacitance. One of its two plates is given $+2\mu \text{C}$ charge and the other plate, $+4\mu \text{C}$ charge. The potential difference developed across the capacitor is,

The equation $x^2+y^2-12x-8y+27=0$ is equivalent to

A lift with 7 people stops at 10 floors. People varying from zero to 7 go out at each floor. The number of ways in which the lift can get emptied, assuming each way only differ by number of people leaving at each floor, is_______.

Two bodies $m_1$ and $m_2$ are kept on a rough horizontal table having coefficient of friction $\mu$ and are joined by a spring. Initially, the spring is in its relaxed state. Find the minimum force $F$ which will make the other block $m_2$ move. ($k$ is the spring constant).

A table with smooth horizontal surface is rotating at a speed $\omega$ about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance $e$ from the center. Find the speed $v$ of the particle with respect to the table as its distance from the center becomes $l$.

Gauss law and it's application

Two particles of mass $m$ and $2m$ have a perfectly inelastic collision. Before collision velocity of $m$ is $u\hat{i}$ and velocity of $2m$ is $-\frac{u}{2}\hat{i}$. Loss of kinetic energy will be

a ball is thrown vertically upwards with velocity of 25 m/s from the top of Tower of height 30m. how long it will take to travel before it hits the ground? g=10m/s^2

A bullet of mass $0.01\text{kg}$ is fired from a gun weighing $2\text{kg}$. Calculate the velocity with which the gun recoils if $10$ bullets are fired at the same time with a speed of $250\text{m/s}$. Consider $+vex$ axis along the direction of firing.