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A person (40 kg) is managing to be at rest between two vertical walls by pressingone wall A by his hands and feet and the other wall B by his back (figure 6-E11). Assume that the frictioncoefficient between his body and the walls is 0.8 and that limiting friction acts at all the contacts. (a) show that the person pushes the two walls with equal force. (b) Find the normal force exerted by either wall on the person. Take $g=10m/s^2$

Rain is falling downwards with a velocity of $3\text{km/h}$. A man walks in the rain with a velocity of $4\text{km/h}$. Raindrops will appear to be falling on the man with a velocity of

The atmosphere is held to the earth by_________.

A homogenous solid cube of side length L is immersed such that it floats at the liquid-liquid interface with length $\frac{L}{4}$ in the denser liquid as shown in figure. The density of the solid is given by

If a radio receiver is tuned to 885 kHz radio wave, the frequency of local oscillator in kHz is

A vector which bisects the angle between

You are given three circuit elements X, Y and Z. When the element X is connected across an a.c. source of a given voltage, the current and the voltage are in the same phase. When the element Y is connected in series with X across the source, voltage is ahead of the current in phase by $\pi /4$.But the current is ahead of the voltage in phase by $\pi /4$ when Z is connected in series with X across the source. Identify the circuit elements X, Y and Z.When all the three elements are connected in series across the same source, determine the impedance of the circuit.

Draw a plot of the current versus the frequency of applied source and mention the significance of this plot.

One mole of an ideal gas goes through the process $P=\frac{2V^2}{1+V^2}$. Then, the change in temperature (in $\text{K}$) of the gas when volume changes from $1{\text{m}}^3$ to $2{\text{m}}^3$ is

The sides of a triangle are respectively 7 cm, $4\sqrt{3}$cm and $\sqrt{1}3$cm, then the smallest angle of the triangle is

An opaque sphere of radius R lies on a horizontal plane. On the perpendicular through the point of contact there is a point source of light a distance R above the sphere then area of shadow on the plane is

A solid cube is placed on a horizontal surface. The coefficient of friction between them is $\mu$, where $\mu <1/2$. A variable horizontal force is applied on the cube's upper face, perpendicular to one edge and passing through the mid-point of the edge, as shown in figure. The maximum acceleration with which it can move without toppling is

Four particles, each of mass $m$ and equidistant from each other, move along a circle of radius $r$ under the action of their mutual gravitational attraction. The speed of each particle is :

A $10\text{kg}$ iron bar (specific heat $0.11{\text{cal/g}}^{\circ }\text{C}$) at ${80}^{\circ }\text{C}$ is placed on the block of ice. How much ice melts?
(Take latent heat of fusion as $80\text{cal/g}$)

The time period of a simple pendulum, whose bob is a hollow metallic sphere is T. Time period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?

Figure shows three forces applied to a trunk that moves leftward by $3$ m over a smooth floor. The force magnitudes are $F_1=5N,F_2=9N,$ and $F_3=3N$. The net work done on the trunk by the three forces

Work done for the process A$\to$ B shown in the figure is

The angular speed of a flywheel making $120\text{revolutions /minute}$ is

Let a pring with force constant k is compressed by $x_1$. Stored potential energy of the spring $U_1$ = $\frac{1}{2}$ k $x^2$ . Let it be further compressed by $x_2$. Let it be further compressed by $x_2$ . Change in potential energy of the spring

Three rods of equal lengths are joined to form an equilateral triangle $\text{PQR}$ as shown in the figure. $\text{O}$ is the mid point of $\text{PQ}$ and distance $\text{OR}$ remains same for any small change in temperature. If the coefficient of linear expansion for $\text{PR}$ and $\text{RQ}$ is same i.e, ${\alpha }_2$, but that for $\text{PQ}$ is ${\alpha }_1$, then which of the following options correctly represents the relation between ${\alpha }_1$ and ${\alpha }_2$?

Find the moment of inertia of 3 rods each of mass $M$ and length $L$, connected to form an equilateral triangle about $MN$

Two particles A and B of masses 1 kg and 2 kg respectively are kept 1 m apart and are released to move under mutual attraction. Find the speed of A when that of B is 3 cm/hour. What is the separation between the particles at this instant?

A barometer tube reads $76\text{cm}$ of $\text{Hg}$. If the tube is gradually inclined at an angle of ${30}^{\circ }$ with horizontal, then find the length of the mercury column in the barometer tube.

If $c_p$ and $c_v$ denotes the specific heat of nitrogen at constant pressure and constant volume respectively, then

A magnet is suspended horizontally in the earth’s magnetic field. When slightly displaced, it oscillates in the horizontal plane with a period T. If a piece of wood having the same moment of inertia as the magnet is attached to the magnet, the new period of oscillation is

Standing waves result from the superposition of two waves that have:

The area under the curve $y=x$ and $y^2=16x$ is

If the speed of a particle is given as $v=6t^2+2t\text{m/s}$, the speed of the particle at $2\text{sec}$ and the average speed in $4\text{sec}$ respectively is

During the photo electric effects electrons get ejected due to photons.if this process continues then at a certain point of time all the electrons should be ejected out.and thus even could affect the stability of the metal itself.but in real life it dose not happen.why?

The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition.

A large horizontal surface is in $SHM$ with an amplitude of $1\text{cm}$. A mass of $10\text{kg}$ is kept gently on it when it is at mean position. For the mass to always remain in contact with the surface, the maximum frequency of $SHM$ will be

How many of the 5 values will be required to infer the remaining?

A stone ties to the end of a string 1m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone

The radii of two soap bubbles are r ₁ and r ₂. In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by

A long cylindrical glass vessel has a small hole of radius 'r' at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath (surface tension T) without any water entering inside is

A circular loop carrying a current of 1.0 A is oriented in a magnetic field of 0.35 T. The loop has an area of 0.24 m² and is mounted on an axis, perpendicular to the magnetic field, which allows the loop to rotate. If the plane of the loop is oriented parallel to the field, what torque is created by the interaction of the loop current and the field?

In given figure, all surfaces are smooth and frictionless. Spring is compressed by $2\text{m}$ and then released. Maximum distance travelled by the block over the inclined plane is
(Take $g=10{\text{m/s}}^2$)

A ball is dropped from a height $h$ on to a floor. If in each collision its speed becomes $e$ times of its striking value, then total change in momentum of ball when it stops rebounding is (Here, $e$ is coefficient of restitution between the ball and the floor)

The binding energies per nucleon of deuteron $\left({}_1{H}^2\right)$ and helium atom $\left({}_{2}H{e}^4\right)$ are $1.1\text{MeV}$ and $7\text{MeV}$. If two deuteron atoms react to form a single helium atom, then the energy released is

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?

A car is moving from A to B in straight line at constant acceleration. If velocities at A and B are u and v respectively, then velocity at the midpoint of A and B is

A particle is projected up the incline such that its component of velocity along the incline is $10\text{m/s}$. Time of flight is $2\text{sec}$ and maximum height above the incline is $5\text{m}$. Then velocity of projection will be

The coefficient of linear expansion of brass and steel are
${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $l_1$ and steel rod of length $l_{2}at{0}^{\circ }C,$ their difference in length $(l_2-l_1)$will remain the same at a temperature if

One gram of pulverised wood burns faster than one gram of log of wood. Why?

What is the Young's modulus for a perfect rigid body?

A thin disc of mass M and radius R has mass per unit area $\sigma \left(r\right)=k{r}^2$, where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

A block of mass $m$ slides down an inclined plane of inclination $\theta$ with uniform speed. The coefficient of friction between the block and the plane is $\mu$. The contact force between the block and the plane is