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Three capacitors of capacitance $3\mu \text{F},10\mu \text{F}$ and $15\mu \text{F}$ are connected in series to a battery of $100\text{V}$. The voltage across $10\mu \text{F}$ is

A spring which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is $W_1$ and in the second case is $W_2$. Then:

The left end of a copper rod (length = 20 cm , area of cross section = 0.20 $c{m}^2$) is maintained at ${20}^{\circ }C$ and the rightend is maintained at ${80}^{\circ }C$. Neglecting any loss of heat through radiation, find (a) the temperature at a point 11 cm from the left end and (b) the heat current through the rod. Thermal conductivity of copper = $385W{m}^{-1\circ }{C}^{-1}$.

A power transmission line feeds input power at $2300\text{V}$ to a step-down transformer with its primary windings having $4000$ turns. What should be the number of turns in the secondary coil in order to get output power at $230\text{V}$?

Block A is placed on block B, whose mass is greater than that of the A. There is friction between the blocks, while the ground is smooth. A horizontal force P, increasing linearly with time, begins to act on A. The accelerations $a_1$ and $a_2$ of A and B respectively are plotted against time (t). Choose the correct graph.

A boy walks to his school at a distance of $6\text{km}$ with constant speed of $2.5{\text{km h}}^{-1}$ and walks back with a constant speed of $4{\text{km h}}^{-1}$. His average speed for round trip in ${\text{kmh}}^{-1}$, is

Protons are projected with an initial speed, $u={10}^4\text{m/s}$ into a region where a uniform electric field $\overrightarrow{E}=-720\hat{j}\text{N/C}$ is present, as shown in figure. The protons are to hit a target that lies at a horizontal distance of $1.3\text{mm}$ from the point where the protons are launched. Find the total time of flight for $\theta ={37}^{\circ }$.

An arc of radius $r$ carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle of $\pi /3$ at the centre. What is electric potential at the centre?

1. 24.47

A point charge $q_1=9.1\mu \text{C}$ is held fixed at origin. A second point charge $q_2=-0.42\mu \text{C}$ and a mass $3.2\times {10}^{-4}\text{kg}$ is placed on the $\text{x-axis}$, $0.96\text{m}$ from the origin. The second point charge is released at rest. What is its speed when it is $0.24\text{m}$ from the origin?

1. 1242

What is the bulk modulus of oxygen if $32\text{g}$ of oxygen occupies $22.4\text{L}$ volume and the speed of sound in oxygen is $320\text{m/s}$ ?

A conductor lies along the $z$ - axis at $-1.5\le z<1.5\text{m}$ and carries a fixed current of $10.0\text{A}$ in $-{\hat{a}}_z$ direction (see figure). For a field $\overrightarrow{B}=3.0\times {10}^{-4}{e}^{-0.2x}{\hat{a}}_y\text{T}$ , find the power required to move the conductor at constant speed to $x=2.0\text{m},y=0\text{m}$ in $5\times {10}^{-3}\text{s}$. Assume parallel motion along the x - axis.

A parallel plate capacitor has a plate area $100{\text{cm}}^2$ and separation $1\text{mm}$. After filling the region between the plates with a dielectric, the capacitor is able to hold charge of $0.12\mu \text{C}$ when connected to a $120\text{V}$ battery. The dielectric constant of the dielectric is

For a spring block system as shown in figure, a time varying force $F=5t\text{N}$ is applied on mass $2\text{kg}$. After $10\text{seconds}$, velocity of $3\text{kg}$ mass is $30\text{m/s}$. Find the velocity of $2\text{kg}$ mass at this instant.

A projectile thrown with velocity $v$ making angle $\theta$ with vertical gains maximum height $H$ in the time for which the projectile remains in air, the time period is

An incompressible fluid is flowing in a cylindrical pipe of internal diameter $4cm$ with a velocity of $5m/s$. If this tube is joined with another tube of internal diameter $2cm$, then the velocity of flow of fluid in the smaller tube will be

Suppose
the spheres A and B in Exercise 1.12 have identical sizes. A third
sphere of the same size but uncharged is brought in contact with the
first, then brought in contact with the second, and finally removed
from both. What is the new force of repulsion between A and B?

A body rotates about fixed axis with an angular acceleration of $3{\text{rad/s}}^2$. Through what angle does it rotate during the time in which its angular velocity increases from $15\text{rad/s}$ to $45\text{rad/s}$ ?

When a sound wave of frequency $300Hz$ passes through a medium, the maximum displacement of a particle of the medium is $0.1cm$. The maximum velocity of the particle is equal to

In the figure shown for given values of $R_1$ and $R_2$ the balance point for jockey is at $40\text{cm}$ from $\text{A}$. When $R_2$ is shunted by a resistance of $10\Omega$, balance shifts to $50\text{cm}$. $R_1$ and $R_2$ are

$[\text{AB}=1\text{m}]$

The number of particles n crossing a unit area perpendicular to the x – axis in unit time can be written as $n=p\frac{(n_2-n_1)}{(x_2-x_1)}$ where $n_1$ and $n_2$ are number of particles per unit volume between length $(x_2-x_1)$. The dimensions of p are

A ball is thrown upwards from the bottom of a fixed chamber of height $20\text{m}$ with a speed of $10\text{m/s}$. The interior of the chamber has no gravity. The ball strikes the ceiling of the chamber and rebounds. After $6\text{seconds}$, gravity is reintroduced in the chamber. The movement of the ball gradually slows down over time and the ball comes to rest. Which of the following is the correct displacement vs time graph for the movement of the ball inside the chamber?

The velocity by of the most energetic electrons emitted from a metallic surface is doubled when the frequency $\nu$ of the incident radiation is doubled. The work function of the metal is-

A body is traveling down an inclined plane of angle of ${30}^{\circ }$ with an acceleration of $2m/s^2$, leaves it with speed of $20m/s$. If the inclined plane is located at a certain height above the ground, find its velocity when it travels in the horizontal direction after $1\text{second}$.