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Find the surface energy of water kept in a cylindrical vessel of radius 6 cm. Surface tension of water = 0.075 J/m²

At what distance a point P, which is located at the base of the rectangular slab of thickness t and refractive index n, will appear when seen from the top ?

Four charges $+q,-q,+q$ and $-q$ are placed in order on the four consecutive corners of a square of side $a$. The work done in interchanging the positions of any two neighbouring charges of the opposite sign is

The three vectors $\overrightarrow{A}=3\hat{i}-2\hat{j}+\hat{k},\overrightarrow{B}=\hat{i}-3\hat{j}+5\hat{k}$ and $\overrightarrow{C}=2\hat{i}+\hat{j}-4\hat{k}$ form

Match List-I with List-II

In a series $LC$ circuit, the applied voltage is $V_0$. If frequency is very low, then the voltage drop across the inductor $V_L$ and capacitor $V_C$ are

A mass m of a perfect gas at pressure $p_1$ and volume $V_1$ undergoes an isothermal process. The final pressure is $p_2$ and volume is $V_1$. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is

Volume of a monoatomic gas varies with temperature as shown in the figure.

Ratio of heat taken by gas and work done by gas is

When the road is dry and coefficient of static friction is $\mu$, the maximum speed of a car in the circular path is $10m{s}^{-1}$. If the road becomes wet and ${\mu }^{\prime }=\frac{\mu }{2}$, what is the maximum permitted speed for the car?

Describe the motion depicted in the given below graphs.

A vessel of volume $2{\text{m}}^3$ contains an ideal gas at pressure ${10}^5{\text{N/m}}^2$ and temperature $300\text{K}$. The gas is continously pumped out of this vessel at a constant volume rate $\frac{dV}{dt}=2\times {10}^{-3}{\text{m}}^3/\text{s}$ , keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find the time taken before half of the original gas is pumped out (in minutes).

Can we state hooke's law as

It states that strain applied on a string is directly proportional to its stress?

A battery consist of a variable number of $n$ identical cells having internal resistance $r$ each. They are connected in parallel. The terminal of battery is short-circuited and the current $I$ is measured. Which of the following graphs give correct relationship between $I$ and $n$?

If the series limit frequency of the Lyman series is $v_L,$ then the series limit frequency of the Pfund series is

A bob of simple pendulum is suspended by a metallic wire. If the length of simple pendulum is increased four times of its initial value. Find the time period with respect to its previous value.

A hollow vertical cylindrical structure rotates about its axis. Tom is standing on a horizontal platform against inner wall of cylindrical structure. At a certain angular speed of hollow cylinder, the horizontal platform below him is removed but he remains stationary against the inner wall. If the radius of the hollow cylinder is $5\text{m}$ and the coefficient of static friction between the cylindrical wall and Tom is $0.15$, find the minimum angular speed of the cylindrical structure at which the platform may be removed.
[Take $g=10{\text{m/s}}^2$]

Water rises in a vertical capillary tube up to $2\sqrt{2}\text{cm}$. If the tube is inclined at an angle ${\theta }^{\circ }$, the length of water risen in the tube is $4\text{cm}$. Find the value of $\theta$.

The gravitational field in a region is given by $\overline{E}=\left(20Nk{g}^{-1}\right)(\hat{i}+\hat{j})$.Find the gravitational Potential at the origin (0,0) in $Jk{g}^{-1}$

The speed of sound as measured by a student in the laboratory on a winter day is $340m{s}^{-1}$ when the room temperature is ${17}^{\circ }C$. What speed will be measured by another student repeating the experiment on a day when the room temperature is ${32}^{\circ }C$ ?

A car is moving with initial velocity $u=3\text{m/s}$ and acceleration $a=2m/s^2$ then, the displacement of car in $6^{th}$ second is

In the figure shown, find the capacitance between points $\text{A}$ and $\text{B}$, if the area of each plate is $A$ and separation between the adjacent plates is $d$.

A solid sphere of radius ${}^{\prime }{a}^{\prime }$ and mass ${}^{\prime }{m}^{\prime }$ rolls along the horizontal plane with constant speed $v_o$. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the iclined plane, sphere will travel (along the incline)?

Calculate the mass flow rate of glycerin of density $1.25\times {10}^3{\text{kg/m}}^3$ through the conical section of a horizontal pipe, if the radii of its ends are $0.1\text{m}$ and $0.04\text{m}$ and pressure drop across its length is $10{\text{N/m}}^2$.

A steel ball of diameter $60mm$ is initially in thermal equilibrium at ${1030}^{\circ }C$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at ${30}^{\circ }C,$ with convective heat transfer coefficient $h=20W/m^{2}K.$ The thermo-physical properties of steel are : density $\rho =7800kg/m^2,$ conductivity $k=40W/mK$ and specific heat $c=600J/kgK.$ The time required in seconds to cool the steel ball in air from ${1030}^{\circ }C$ to ${430}^{\circ }C$ is

A Conductor with rectangular cross-section has dimensions $(a\times 2a\times 4a)$ as shown in figure. Resistance across $\text{AB}$ is $x,$ across $\text{CD}$ is $y$ and across $\text{EF}$ is $z.$ Then

A block $A$ is placed on a smooth horizontal surface and a particle $C$ is suspended with the help of light rod from point $B$ of the block as shown. Now both the block $A$ and the particle $C$ are given velocity $v_0$ towards left. The block $A$ strikes a fixed wall and suddenly stops. Then the smallest velocity $v_0$ for which the particle $C$ will swing in a full circle about the point $B$ is
(The rod $BC$ is free to rotate about $B$ and $B$ is attached to block $A$)