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In a power plant, water (density $=1000kg/m^3$) is pumped from $80kPa$ to $3MPa$. The pump has an isentropic efficiency of $0.85$. ssuming that the temperature of the water remains the same, the specific work (in $kJ/kg$) supplied to the pump is

Initially the spheres $\text{A}$ and $\text{B}$ are at potential $V_A$ and $V_B$. The potential of sphere $\text{A}$ when sphere $\text{B}$ is earthed is

A wire carrying current $i$ is in the shape of a plane curve given by $r=f\left(\theta \right)$ where the $r$ and $\theta$ are polar coordinates. The magnetic field at the center of curvature of the current carrying wire is

A jar is filled with two non - mixing liquid 1 and 2 having densities ${\rho }_1$ and ${\rho }_2$ respectively. A solid ball, made of a material of density ${\rho }_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho }_1,{\rho }_2$ and ${\rho }_3$?

In hydrogen atom, if the difference in the energy of the electron in $n=2$ and $n=3$ orbits is $E$, the ionization energy of hydrogen atom is

Three blocks of masses $2\text{kg}$, $4\text{kg}$ and $6\text{kg}$ are connected by strings and placed on a fricitionless incline of ${53}^{\circ }$ as shown. A force of $120\text{N}$ is applied upward along the incline on the $6\text{kg}$ block so that system accelerates. If the strings are ideal, the ratio tension in the strings $\frac{T_1}{T_2}$ will be $(g=10{\text{ms}}^{-2})$

A circular copper-ring of radius r translates in its pl ane with a constant velocity v. A uniform magnetic field B exists in the space in a direction perpendic ular to the planne of the ring. Consider different pairs of diametrically opposite points on the ring.

(a) Between which pair of points is the emf max imum ? What is the value of this maximum emf ?

(b) Between which pair of points is the emf mini mum ? What is the value of this minimum emf ?

The velocity gradient at a distance $100mm$ from the boundary if the velocity profile is a parabola with the velocity at $200mm$ from the boundary between the boundary layer and free stream flow be $2m/s$ is $se{c}^{-1}$

A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up . Find the force when the man is at a depth h.

A 100 kW, 500 V, 2000 rpm separately excited dc motor is energized from 400 V, 50 Hz, $3-\varphi$ source through a $3-\varphi$ full converter. The voltage drop in conducting thyristor is 1 V. The dc motor has following parameters:

$r_a=0.2\Omega K_m=1.6\text{V-s/rad}{L}_a=8mH$

Rated armature current = 210 A.

The value of firing angle of converter for speed of 2000 rpm so that motor draws rated armature current and its respective supply side power factor will be

The activity of a radioactive sample is $A_1$ at time $t_1$ and $A_2$ at time $t_2$. If $\tau$ is average life of sample then the number of nuclei decayed in time $(t_2–t_1)$ is

Two particles of equal mass have co-ordinates $(2,4,6)\text{m}$ and $(6,2,8)\text{m}$. One particle has a velocity ${\overrightarrow{v}}_1=\left(2\hat{i}\right)\text{m/s}$ and another particle has velocity ${\overrightarrow{v}}_2=\left(2\hat{j}\right)\text{m/s}$ at time $t=0$. The coordinates of the centre of mass of the system at time $t=1\text{s}$ will be

Initially switch $S$ is in open state. How much charge flows through switch $S$ when it is closed? Assume steady state condition to be achieved after $S$ closed.

Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height $h_0$ and pressure $2P_0$ where $P_0$ is the atmospheric pressure. There is a hole in the wall of the tank at a depth $h_1$ below the top from which water comes out. A long vertical tube is connected as shown.


Find the height $h_2$ of the water in the long tube above the top initially.

A simple pendulum has a time period of 3.0 s. If the point of suspension of the pendulum starts moving vertically upward with a velocity v = kt where $k=4.4m{s}^{-2}$, the new time period will be (Take g = 10 $m{s}^{-2}$

For the given uniformly charged ring, magnitude of the net electric field at point $\text{P}$ is

A right-angled prism is to be made by selecting a proper material and the angles $A$ and $B$ $(B\le A)$, as shown in the figure. It is desired that a ray of light incident on the face $AB$ emerges parallel to the incident direction after two internal reflections. What should be the minimum refractive index above which the internal reflections happens?

In the arrangement of three blocks as shown in figure, the string is inextensible. If the directions of accelerations are as shown in the figure, then determine the constraint relation.

Three particles $\text{A, B}$ and $\text{C}$ each of mass $m$ are lying at the corners of an equilateral triangle of side $L$. If the particle $\text{A}$ is released, keeping the particles $\text{B}$ and $\text{C}$ fixed, the magnitude of instantaneous acceleration of $\text{A}$ is

An electric bulb is rated as $10\text{W},220\text{V}$. How many of these bulbs can be connected in parallel across $220\text{V}$ supply if the maximum current which can be drawn is $5\text{A}$ ?

Bro in chapter of magnetic effect of current to find a directionof magnetic feildfin coil we use right hand thambtrule but here lenzes law you are telling that right hand thumb rule use to find the direction of area vactor I am confused between two things

A quantity of heat required to change the unit mass of a solid substance, from solid state to liquid state, while the temperature remains constant, is known as the _______.

The magnetic field $B$ shown in the figure is directed into the plane of the paper. $\text{ACDA}$ is a semicircular conducting loop of radius $r$ with the centre at $\text{O}$. The loop is now made to rotate clockwise with a constant angular velocity $\omega$ about an axis passing through $O$ and perpendicular to the plane of the paper. The resistance of the loop is $R$. Obtain an expression for the magnitude of the induced current in the loop.