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The stream of a river is flowing at a speed of $2km/h$. A swimmer can swim at a speed of $4km/h$ in still water. What should be the direction of the swimmer with respect to the flow of the river to cross the river with minimum drift?

Moment of inertia of the system of two rods having same linear mass density $\lambda$, about the axis $AB$ as shown in the figure is

When a uniform solid sphere and a disc of the same mass and of the same radius rolls down without slipping on an inclined plane from rest to the same distance along the inclined plane, then the ratio of the time taken by solid sphere and the disc to cover the distance is

The lowest frequency of light that will cause the emission of photoelectrons from the surface of a metal (for which work function is 1.65 eV) will be

In the shown figure, the block moves downwards with velocity $V_1$, the wedge moves rightwards with velocity $V_2$. Assuming the surface to be smooth and pulley and string to be ideal, the correct relation between $V_1$ and $V_2$ is

For a constant volumetric stress on an object, the fractional change in the object volume $\left(\frac{\Delta V}{V}\right)$ and its bulk modulus $\left(B\right)$ are related as

The work done by an external agent in stretching a spring of force constant $K$ from length $l$ to $3l$ is

A particle is moving along positive $x$-axis and at $t=0$, the particle is at $x=0$. The acceleration of the particle is a function of time. The acceleration at any time $t$ is given by $a=2(1–[t\left]\right)$ where $\left[t\right]$ is the greatest integer function . Assuming that the particle is at rest initially, the average speed of the particle for the interval $t=0s\text{to}t=4s$ is

The mass number of a nucleus is

A single slit of width 0.20 mm is illuminated with light of wavelength 500 nm. The observing screen is placed 80 cm from the slit. The width of the central bright fringe will be

[AMU (Med.) 2002]

Two plane mirrors are placed at an angle of ${120}^{\circ }$ and a man combing his hair is standing at an asymmetric position. How many images will he see?

On the cylinder of radius R in the figure, which is rolling with velocity of centre of mass $v=\frac{\omega R}{4}$ towards right ($\omega$ is clockwise), find the velocities (magnitude) at points A, B, C, D.

A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current $I_1\left(t\right)$ starts flowing through the coil. If $I_2\left(t\right)$ is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to $I_1\left(t\right)$, then the product of $I_2\left(t\right)$ and B(t)

By increasing the temperature, the specific resistance of a conductor and a semiconductor

What is the current in the circuit shown below

An ideal gas at 300 K occupies a volume of 0.5 $m^3$ at a pressure of 2 atm. The gas expands adiabatically until its volume is 1.2 $m^3$. Next, the gas is compressed isobarically to its original volume. Finally, the pressure is increased isochorically until the gas returns to its initial state. Represent the change on the P-V diagram. Determine the temperature at the end of each transformation; and the work done during the cycle. Assume g = 1.4.

If $\overrightarrow{a}=2\hat{i}+4\hat{j}+3\hat{k},\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k},$ then the scalar product and the angle between them are

Liquid reaches an equilibrium as shown in a capillary tube of internal radius $r=1\text{cm}$. If the surface tension of the liquid is $T=0.07\text{N/m}$. The angle of contact $\theta ={60}^{\circ }$ and density of liquid $\rho ={10}^3{\text{kg/m}}^3$, then the pressure difference between $P$ and $Q$ is





Take atmospheric pressure as ${10}^5{\text{N/m}}^2$.

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5\text{m/s}$. What is the height of the plane of circle from vertex of the funnel?

The binding energy per nucleon of ${}_1^{2}H$ and ${}_2^{4}He$ are $1.1MeV$ and $7.0MeV$ respectively. Energy released in the process ${}_1^{2}H{+}_1^{2}H{\to }_2^{4}He$ is

A 5kg block is tied to a 1m string and is rotated with a constant angular velocity of 2 rad/sec in the horizontal plane. Find the linear momentum of the block.

A large steel wheel is to be fitted on a shaft of the same material. At $27{}^{\circ }\text{C}$, the outer diameter of the shaft is $8.70\text{cm}$ and the diameter of the central hole of the wheel is $8.69\text{cm}$. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on it?

$[\alpha =1.20\times {10}^{-5}/{}^{\circ }\text{C}]$

Two condensers, one of capacity $C$ and other of capacity $\frac{C}{2}$ are connected to a $V$ - volt battery as shown in the figure. The work done in charging both the condensers fully is

3 A of current is flowing in a linear conductor having a length of 40 cm. The conductor is placed in a magnetic field of strength 500 gauss and makes an angle of with the direction of the field. It experiences a force of magnitude

[MP PET 1993]

Light of wavelength $5000\stackrel{\circ }{A}$ is falling on a photo sensitive surface. If the surface has received ${10}^{-7}$J of energy, then the number of photons falling on the surface will be

A ship is travelling due east at $10\text{km/hr}$. Another ship heading ${30}^{\circ }$ east of north is always due north from the first ship. The speed of the second ship in $\text{km/hr}$ is

A horizontal platform is executing simple harmonic motion in the vertical direction of frequency v. A block of mass m is placed on the platform. What is the maximum amplitude of the platform so that the block is not

detached from it ?

A ball initially at rest, is dropped from building of height $10\text{m}$ to ground as shown in the figure below. If the coefficient of restitution is $e=0.7$ and after collision, the ball rebounds back up to height $h$, find the value of $h$. (Take $g=9.8{\text{m/s}}^2)$

Two vessels separately contains two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ being twice that of $B$. Under such conditions, the density of $A$ is found to be $1.5$ times the density of $B$. The ratio of molecular weight of $A$ and $B$ is

A person in a wheelchair is moving up a ramp constant speed. Their total weight is 900N. The ramp makes an angle ${37}^{\circ }$ with the horizontal. Calculate the component of its weight parallel and perpendicular to the ramp.

A block of mass $100\text{kg}$ is attached to the back of a truck with the help of a spring. The frictional coefficient between the truck and the block is $0.2$ (take ${\mu }_s={\mu }_k)$. Acceleration of the truck is $5{\text{m/s}}^2$ and the spring elongates by a distance of $1\text{cm}$. If the block is just about to slip, what is the force constant of the spring? Take $g=10{\text{m/s}}^2$.

A block of mass $1\text{kg}$ is kept on an inclined accelerating conveyor belt. Acceleration of the belt is $1{\text{m/s}}^2$ as shown in figure. Minimum coefficient of static friction between the belt and block to prevent slipping of the block will be: [Take $g=10{\text{m/s}}^2$]

In the figure given below, two blocks of mass $m$ and $M$ are connected through a light inextensible rope. Then, find the tension in the connecting rope. Consider coefficient of static friction between the inclined surface and the blocks to be $\mu$.

A liquid is filled in a container which is kept in a room whose temperature is ${20}^{\circ }\text{C}$. When temperature of liquid is ${80}^{\circ }\text{C}$, it emits heat at the rate of $45{\text{cal s}}^{-1}$. When temperature of liquid falls of ${40}^{\circ }\text{C}$, using Newtons law of cooling, its rate of heat loss will be

A particle of mass $10\text{g}$ moves along a circle of radius $6.4\text{cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle is equal to $8\times {10}^{-4}\text{J}$, by the end of the second revolution (after the beginning of the motion)?

From a planet of mass $16M$ and radius $4R$, we wish to send an object to its moon of mass $M$ and radius $R$. Distance between centres of planet and moon is $10R$. Minimum speed at which object should be projected from the surface of planet so that it reaches moon is (Assume that the planet and the moon are at rest)

A ball of mass $5\text{kg}$ is dropped from a cliff of height $75\text{m}$. What is the ratio of the kinetic energy to the potential energy of the ball when it reaches the halfway point of the fall?

Which graph describes motion of point $P$ on the disc, initially at origin?

Two bodies $A$ & $B$ rotate about an axis such that angle ${\theta }_A$ (in radians) covered by first body is proportional to square of time, & ${\theta }_B$ (in radians) covered by second body varies linearly. At $t=0,{\theta }_A={\theta }_B=0$. If $A$ completes its first revolution in $\sqrt{\pi }\text{s}$ & $B$ needs $4\pi \text{s}$ to complete half revolution, then angular velocities ${\omega }_A$ & ${\omega }_B$ at $t=5\text{s}$ are in the ratio

If $\alpha \text{kilogram}$, $\beta \text{meter}$, and $\gamma \text{second}$ are the fundamental units, $1\text{cal}$ can be expressed in new units as $[1\text{cal}=4.2\text{J}]$

If the speed of a particle is given as $v=3t^2+5\text{m/s}$, the speed of the particle at $4\text{sec}$ and the average speed in $4\text{sec}$ respectively is

Two circular discs of moment of inertia $0.4{\text{kg-m}}^2$ and $0.6{\text{kg-m}}^2$ are rotating about their own axis (vertical axis passing through geometric centre) at the rate of $200\text{rpm}$ and $50\text{rpm}$ both in clockwise direction. If both are gently brought in contact to rotate about same axis, the angular speed of the combination is

Spacing between two successive nodes in a standing wave on a string is $x$. If tension in the string is doubled keeping frequency constant, then find the new spacing between successive nodes.