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In figure shows an aluminium rod joined to a copper rod. Each of the rods has a length of 20 cm and area of cross section $0.20c{m}^2$. The junction is maintained at a constant temperature ${40}^{\circ }$ and the two ends are maintained at ${80}^{\circ }$. Calculate the amount of heat taken out from the cold junction in one minute after the steady state is reached. The conductivities are $K_{Al}=200W{m}^{-1\circ }{C}^{-1}$ and $K_{Cu}=400W{m}^{-1\circ }{C}^{-1}$

${40}^{\circ }C{80}^{\circ }C\begin{array}{cc}\text{Aluminium}& \text{Copper}\end{array}{80}^{\circ }C$

Two thermally insulated vessels $1$ and $2$ are filled with air at temperature ($T_1$, $T_2$), volume ($V_1$, $V_2$) and pressure ($P_1$, $P_2$) respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

A ray of light falls on the surface of a spherical glass paper weight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$. The angle of deviation of the emergent ray from the direction of the incident ray is

A hemispherical portion of the surface of a solid glass sphere (p rt: 1.5) of radius r is silvered to make the inner side reflecting. An object is placed on the axis of the hemisphere at a distance 3r from the centre of the sphere. The light from the object is refracted at the unsilvered part, then reflected from the silvered part and again refracted at the unsilvered part. Locate the final image formed.

Calculate the moment of Inertia of uniform solid sphere of mass $M$ and Radius $R$, about its diameter

The gain factor of an amplifier is increased from 10 to 12 as te load resistance si changed from $4k\Omega$ to $8k\Omega$ Calculate (a) the amplification factor and (b) the plate resistance.

A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-4Q$, the new potential difference between the same two surfaces is

The magnitude of the resultant of two forces each having magnitude $F_0$ and angle between them is ${120}^o,$ is $xF.$ Then $x$ is

In an agricultural experiment, a solution containing 1 mole of a radioactive material $(t_{\frac{1}{2}}$, = 14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit, if the activity measured was $1\mu Ci$, what per cent of activity is transmitted from the root to the fruit in steady state?

Consider the following two statements:

A . Linear momentum of a system of particles is zero. B. Kinetic energy of a system of particles is zero.

If the energy of the photon is increased by a factor of 4, then its momentum

The resultant of two forces having magnitude $3p$ and $2p$ is $R$. If the force having magnitude $3p$ is doubled keeping the same direction, then the resultant is also doubled. The angle between two forces is

Two capillary tubes of the same length but different radii $r_{1}and{r}_2$ are fitted in parallel to the bottom of a vessel. The pressure head is P. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

A disc of mass $m$ is moving with constant speed $v_0$ on a smooth horizontal table. Another disc of same mass is placed on the table at rest as show in the figure. If collision is elastic then find the velocity of the discs after collision.

[Consider $r<<R$]$(\theta =ta{n}^{-1}\frac{h}{\sqrt{R^2-h^2}})$.

An ideal black-body at room temperature is thrown into a furnace. It is observed that

A small particle of mass m is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius a. Motion occurs essentially in horizontal plane (assume gravity free space). The angular velocity of the cord is ${\omega }_0$ when the distance from the particle to the tangency point is $r_0$.

Scissors for cutting cloth have blades that are longer than its handles; but shears for cutting metals have blades are shorter than its handles. This is because

A metallic wire of length L metres extends by l metres when stretched by suspending a weight Mg to it. The mechanical energy stored in the wire is

Two trains are each 50m long moving parallel towards each other at speeds 10m/s and 15m/s respectively,at what time will they pass each other?

The plot of $t_{1/2}v/s[R{]}_0$ for a reaction is a straight-line parallel to x-axis. The unit for the rate constant of this reaction is:

A gas in container A is in thermal equilibrium with identical another gas in container B. Both contain equal masses of the two gases in the respective containers. Which of the following can be true

In which of the following cases forces may not be required to keep the

A cubical block of wood of specific gravity 0.5 and chunk of concrete of specific gravity 2.5 are fastened together.The ratio of mass of concrete to the mass of wood which makes the combination to float its entire volume submerged in water is

Two small metal balls of different mass $m_{1}and{m}_2$ are connected by strings of equal length to a fixed point. When the balls are given charges, the angles that the two strings make with the vertical are ${30}^{\circ }and{60}^{\circ }$, respectively. The ratio $m_1/m_2$ is close to

Boat A is sailing towards north-east with velocity $\overrightarrow{v}=5\hat{i}+5\hat{j}km/hr$, where $\hat{i}$ points east and $\hat{j}$, north. Boat B is at a distance of $50km$ east and $100km$ north of boat A and is sailing towards west at $10km/hr$. A will be at minimum distance from B in:

A force $F=-K(y\hat{i}+x\hat{j})$, where K is a positive constant, acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particle is

A body of mass M is kept on a rough horizontal surface (friction coefficient = $\mu$). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is F, where

In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the

The moment of inertia of a solid hemi-sphere of mass M and radius R about an axis passing through its center of mass and parallel to its circular face is

The current generator $I_g$, shown in figure (38-E19), sends a constant current i through the circuit. The wire cd is fixed and ab is made to slide on the smooth, thick rails with a constant velocity v towards right. Each of these wires has resistance r. Find the current through the wire cd.

Figure (16-E111)shows a person standing somehere in between two identical tuning forks, each vibrating at

512 Hz. If both the tuning forks move towards right at a speed of 5.5 m s^{-1}, find the number of beats heard by the listener. Speed of sound in air =$330m{s}^{-1}$.

Two long conductors separated by a distance $d$ carry currents $i_1$ and $i_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is

A vertical glass capillary tube, open at both ends, contains some water. Which of the following shapes can not be taken by the water in the tube?

A particle of mass m attached to a string of length l is describing circular motion on a smooth plane inclined at an angle $\alpha$ with the horizontal. For the particle to reach the highest point its velocity at the lowest point should exceed :

A capacitor stores $50\mu C$ charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of $100\mu C$ flows through the battery. Find the dielectric constant of the material inserted.

Block $A$ with a kinetic energy of $500\text{J}$ collides with another block $B$ of mass $10\text{kg}$ initially kept at rest. Assuming that the collision is perfectly elastic, what is the final speed of the block $B$?

A short bar magnet with its north pole facing north forms a neutral point at P in the horizontal plane. If the magnet is rotated by ${90}^{\circ }$ in the horizontal plane, the net magnetic induction at P is (Horizontal component of earth’s magnetic field = )

A uniform rod of length $L$ and mass $M$ is held vertical with its bottom end pivoted to the floor. The rod falls under gravity, freely turning about the pivot. If acceleration due to gravity is $g$, what is the instantaneous angular speed of the rod when it makes an angle of ${60}^{\circ }$ with the vertical?

A string is used to pull a block of mass $m$ vertically up by a distance $h$ at a constant acceleration $\frac{g}{4}$. The work done by the tension in the string is

In the figure shown co-efficient of friction between the block B and the block C is 0.4. there is no friction between the block C and the surface on which it is placed. The system of blocks is released from rest in the situation shown in the diagram. Find the distance moved by the block C when block A descends through a distance 2 m. Given masses of the blocks are $m_A$ = 3 kg, $m_B$ = 5 kg and $m_C$ = 10 kg.

In the process ABC for an ideal mono-atomic gas, the temperature at states A and C are equal. The heat released in the process BC is $Q$. Then the work done in the process A to B is equal to ____. (AB is isobaric and BC is isochoric process)

The rate of steady volume flow of water through a capillary tube of length 'l' and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but twice the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)

A particle of mass $m$ moving with velocity $1\text{m/s}$ collides elastically with another particle of mass $2m$ (initialy at rest). If the incident particle is deflected by ${90}^{\circ }$. The angle $\theta$ made by the heavier mass with the initial direction of motion of mass $m$ will be equal to:
(consider collision to be perfectly elastic)

A Carnot engine works between 600 K and 300 K. In each cycle of operation, the engine draws 1000 J of heat energy from the source. In order to increase the efficiency to $70\%$, source temperature will have to be