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The two ends of a metal rod are maintained at temperatures 100${}^{\circ }$C and 110${}^{\circ }$C.The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200${}^{\circ }$C and 210${}^{\circ }$C, the rate of heat flow will be :

The maximum and minimum magnitudes of the resultant of two vectors are 23 units and 7 units respectively. If these two vectors are acting at right angles to each other, the magnitude of their resultant will be

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now

Block of $3\text{kg}$ is initially in equilibrium and is hanging by two identical springs $A$ and $B$ as shown in the figure. If spring $A$ is cut from lower point at $t=0$ then, find acceleration of block in $m{s}^{-2}$ at $t=0$.

Three blocks $A$,$B$ and $C$ weighing $1,8$ and $27\text{kg}$ respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. If $T_3$ is equal to $36\text{N}$, then $T_2$ is

Three moles of an ideal gas ($C_P=\frac{7}{2}R$) at pressure, $P_A$ and temperature $T_A$ is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally gas is compressed at constant volume to its original pressure $P_A$.
The correct $P-V$ and $P-T$ diagrams for the complete process are

The resistance of an ammeter is $13\Omega$ and its scale is made for a current upto 100 amp. After an additional shunt has been connected to this ammeter it becomes possible to measure current upto 750 amp.. The value of shunt resisance is

A conducting ring of mass 2 kg and radius 0.5 m is placed on a smooth horizontal plane. The ring carries a current I=4A. A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in figure. The initial angular acceleration of the ring is

An object is approaching a fixed plane mirror with velocity $10\text{m/s}$ making an angle of ${60}^{\circ }$ with the normal to the mirror. The speed of image with respect to the mirror is

A car has two travellers of masses $m_1$ and $m_2$. If the car moves towards east with acceleration ${}^{\prime }{a}^{\prime }$, find pseudo force on $m_1$ as observed by traveller of mass $m_2$

A block of mass $m$ is placed at rest on the top of a smooth wedge of mass $M$, which in turn is placed at rest on a smooth horizontal surface as shown in figure. Then the distance moved by the wedge as the block reaches the foot of the wedge is

A bucket full of hot water cools from ${75}^{o}Cto{70}^{o}C$ in time $T_1$, from ${70}^{o}Cto{65}^{o}C$ in time $T_2$, and from ${65}^{o}Cto{60}^{O}C$ in time $T_3$ then

Two spherical bodies $A$ and $B$ with a radius of $12\text{cm}$ and $18\text{cm}$ respectively are at temperatures $T_A$ and $T_B$. The maximum intensity in the emission spectrum of $A$ is at $1000\text{nm}$ and in that of $B$ is at $2000\text{nm}$. Considering both bodies to be black bodies, Find the ratio of the rate of total energy radiated by $A$ to that of $B$ ?

The only possibility of heat flow in a thermos flask is through its cork which is 75 $c{m}^2$ in area and 5 cm thick. Its thermal conductivity is 0.0075 $cal/cmse{c}^{o}C$. The outside temperature is ${40}^{o}C$ and latent heat of ice is 80 $cal{g}^{-1}$. Time taken by 500 g of ice at $0^{o}C$ in the flask to melt into water at $0^{o}C$ is

An ideal gas has volume $V_0$ at ${27}^{\circ }C$.It is heated at constant pressure so that its volume becomes $2V_0$. The final temperature is

A small bar A resting on a smooth horizontal plane is attached by thread to a point P and by means of a weightless pulley, to a weight $B$ possessing the same mass as the bar itself. Besides, the bar is also attached to a point 0 by means of a light non-deformed spring of length $l_0=50cm$ and stiffness $k=5mg/l_0,$ where $m$ is the mass of the bar. The thread PA have been burned, the bar starts moving. Find it's velocity at the moment when it is breaking off the plane.

A copper block of mass $2\text{kg}$ is heated to a temperature of ${500}^{\circ }\text{C}$ and then placed in a large block of ice at $0^{\circ }\text{C}$. What is the maximum amount of ice that can melt? The specific heat of copper is $400{\text{J kg}}^{-1}$ ${}^{\circ }{\text{C}}^{-1}$and latent heat of fusion of water is $3.5\times {10}^5{\text{J kg}}^{-1}$.

The maximum range of a projectile is $22\text{m}$. When it is thrown at an angle of ${15}^{\circ }$ with the horizontal, its range will be-

A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega .$ Its centre of mass rises to a maximum height of

Two springs have their force constant as $k_1$ and $k_2(k_1>k_2)$ . When they are stretched by the same force

A string of linear mass density $0.5gc{m}^{-1}$ and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end (figure 15-E4). The nng can move on a vertical rod. A wave pulse is produced, on the string which moves towards the ring at a speed of $20cm{s}^{-1}$. The pulse is symmetric about its maximum, which is located at a distance of 20 cm from the end joined to the ring. (a) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape. (b) The shape of the string changes periodically with time.Find this time period. (c) What is the tension in the string ?

Figure shows the variation in the internal energy U with the volume V of 2.0 mol of an ideal gas in a cyclic process abcda. The temperatures of the gas at b and c are 500 K and 300 K respectively. Calculate the heat absorbed by the gas during the process.

A wheel rotates with a constant angular acceleration of 2.0 $\frac{rad}{s^2}$. If the wheel starts from rest, how many revolutions will it make in the first 10 seconds?

The resistances of an iron wire and a copper wire at 20 ${}^{\circ }$ are 3.9 $\Omega$ and 4.1 $\Omega$ respectively. At what temperature will the resistances be equal ? Temperature coefficient of resistivity for iron is 5.0 ${\times }^{-3}{K}^{-1}$ and for copper it is 4.0 $\times {10}^{-3}{K}^{-1}$. Neglect any thermal expansion.

A box contains $N$ molecules of a perfect gas at temperature $T_1$ and pressure $P_1$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure and temperature are $P_2$ are $T_2$ respectively, then

The light of wavelength 6328 Å is incident on a slit of width 0.2 mm perpendicularly, the angular width of central maxima will be

[MP PMT 1987; Pb. PMT 2002]

A particle is moved from $(0,0)$ to $(a,a)$ under a force $\overrightarrow{F}=(3\hat{i}+4\hat{j})$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the works done by this force along two paths. Then

A wire of length $2L,$ is made by joining two wires $\text{A}$ and $\text{B}$ made of the same material having same length but different radii $r$ and $2r$. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $\text{A}$ is $p$ and that in $\text{B}$ is $q$, then the ratio $p:q$ is:

Find the charge supplied by the battery in the arrangement shown in figure (31-E4).

A Carnot's engine used first an ideal monoatomic gas then an ideal diatomic gas. If the source and sink temperature are ${411}^{\circ }C$ and ${69}^{\circ }C$ respectively and the engine extracts 1000 J of heat in each cycle, then area enclosed by the PV diagram is

If a body describes a circular motion under inverse square field, the time taken to complete one revolution, T is related to the radius of the circular orbit as

A potentiometer wire of length 1 m and resistance $10\Omega$ is connected in series with a cell of e.m.f 2 volt with internal resistance $1\Omega$ and a resistance box including a resistance R. If the potential difference between the ends of the wire is 1 mV, then the value of R will be

A charged particle is accelerated through a potential difference of 12 kV and acquires a speed of $1.0\times {10}^{6}m{s}^{-1}.$ It is then injected perpendicularly into a magnetic field of strength 0.2 T. Find the radius of the circle described by it.

A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, R is equal to

Ram is trying to move a box by pushing it at an angle $\theta$ with a force F${}_1$ (fig 1) while Avinash is trying to move the same box by pulling it with force F${}_2$ (fig 2). Who will have to apply a greater force in order to just move the box. Coefficient of static friction is ($\mu$${}_s$) and coefficient of Kinetic friction. $\mu$${}_k$

A particle is projected with a velocity of $\sqrt{7}{\text{ms}}^{-1}$ at angle ${60}^{\circ }$ with horizontal. Find the average velocity of the projectile between the instants of point of projection and reaching the highest point.

An ideal gas at pressure P is adiabatically compressed so that its density becomes n times the initial value. The final pressure of the gas will be $\gamma =\frac{C_p}{C_v}$,

If $n_1,n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the fundamental frequency n of the original string is given by

A diverging lens, focal length $f_1=20\text{cm}$ is separated by 5 cm from a converging mirror, focal length $f_2=10\text{cm}$. Where should an object be placed from the lens so that a real image is formed at the object itself ?