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Water falls from a height o 500m what is the rise in temp of water at bottom of whole energy remains in the water

Experimental results about diffusion depends on temperature

The force $\left(F\right)$ that needs to be applied on water in the thicker arm so that the water may remain in equilibrum is

A small block of mass $m$ is shot into each of the four smooth tracks as shown in the given option figures. The speed $v$ with which the block enters the track is the same in all cases and it reaches the same height ${}^{\prime }{h}^{\prime }$ on the track in all cases. At the highest point of the track, the normal reaction is maximum in:

Two parallel plate capacitors of capcitances C and 2C are connected in parallel and changed to a potential V by a battery. The battery is then disconnected and the apsce between the plates of capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes

Which of the following graphs correctly represents the variation of $\log {\lambda }_m$ with $\log T$?
[${\lambda }_m$ is the wavelength corresponding to maximum intensity of radiation and $T$ represents absolute temperature.]

For a particle moving along circular path, the radial acceleration $a_r$ is proportional to time $t$. If $a_t$ is the tangential acceleration, then which of the following will be independent of time?

The linear mass density of a rod of length $5\text{m}$ varies with distance from its end fixed at the origin as represented in the graph shown below:

Then find the position of centre of mass of the rod w.r.t origin.

A drop of liquid of diameter $2.8\text{mm}$ break up into $216$ identical drops. What is the approximate change in energy of bigger drop?
(Given: Surface tension of liquid, $T=75\text{dyne/cm}$)

A hollow metal sphere of radius 20 cm is charged such that the potential on its surface is 120 Volt. The potential at the centre of the sphere is

What is the relationship between the mechanical advantage and the velocity ratio for:

1) An ideal machine; 2) A practical machine?

A block of mass $3\text{kg}$ is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be $(g=10{\text{m/s}}^2)$

In the following circuit the potential difference between points X and Y is

The space between two plates $20\text{cm}\times 20\text{cm}\times 1\text{cm},1\text{cm}$ apart is filled with a liquid of viscosity $1\text{Poise}$. The upper plate is dragged to the right with a force of $F=5\text{N}$ keeping the lower plate stationary. The upper plate is moving at a constant speed $u$ as shown in figure.


What will be the velocity in $\text{m/s}$ of the flow at a point $0.5\text{cm}$ below the lower surface of the upper plate if linear velocity profile is assumed for the flow ?

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficient of thermal conductivity $\text{K}$ and $2\text{K}$ and thickness $X$ and $4X$ respectively are $T_2$ and $T_1(T_2>T_1)$. The rate of heat transfer through the slab in a steady state is $\left(\frac{A(T_2-T_1)K}{X}\right)f$, then $f$ is equal to

The spring shown in figure (12.E5) is unstretched when a man starts pulling on the cord. The mass of the block is M. If the man exerts a constant force F, find (a) the amplitude and the time period of the motion of the block, (b) the energy stored in the spring when the block passes through the equilibrium position and (c) the kinetic energy of the block at this position.

A particle of mass $m$ with speed $v$ collide inelastically with the stationary ring and gets embedded in it. Find the angular velocity with which the system rotates after the collision. Assume that the thickness of the ring is much smaller than its radius.

Inside a long straight uniform wire of circular cross - section there is a long cylindrical cavity (bore) of radius r whose axis is parallel to the axis of the wire. Axis of cavity is displaced from the axis of wire by a distance ‘L’ as shown in figure. A direct current J flows through the wire. Then
I) Magnetic field inside the cavity is non-uniform
II) Magnetic field inside the cavity is uniform
III) Field inside the cavity is directly proportional to L
IV) Magnetic field inside the cavity is independent of L

A body is vibrating 6000 times in a minute. If the velocity of sound is 360 m/s. Find

(i) the frequency in (Hz) (ii) Wavelength of sound

The surface tension of a liquid is 80 dyne/cm. Its relative density is 0.8. If the angle of contact between the liquid and glass is ${60}^{\circ }$, find the height to which the liquid rises in a glass capillary tube of radius 1 mm. $(g=10m/s^2)$

In Young’s double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double that from the other slit. If $I_m$ is the maximum intensity, then the resultant intensity when they interfere at a phase difference of $\varphi$ is

The blocks are initially in equilibrium position then the minimum compression in the spring from its natural length so that the block of 2m leaves contact with the surface is $\frac{nmg}{k}$, where n equals to

A small ball of radius $2\text{cm}$ executes SHM in a hemispherical bowl of radius $42\text{cm}$. Find the time period of oscillation. Take $\pi =3.14$ and $g=10{\text{m/s}}^2$

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57{}^{o}C$ is drunk. You can take body (tooth) temperature to be $37{}^{o}C$, ${\alpha }_{Cu}=1.7\times {10}^{-5}{}^{o}C$ and bulk modulus for copper $B_{Cu}=140\times {10}^{9}N/m^2$.

To what tempreture should the hydrogen at ${327}^{\circ }C$ be cooled at constant pressure, so that root mean square velocity of its molecules become half of its previous value

Compute $P\left(A|B\right)$, if $P\left(B\right)=0.6$,$P\left(A\right)=0.2$ and $P(A\cup B)=0.50$.

In an adsorption experiment, a graph between log (x/m) versus log p is found to be linear with a slope of ${45}^{\circ }$. The intercept on log (x/m) axis was found to be 0.3010. The amount of the gas adsorbed per gram of charcoal under a pressure of 0.5 atm will be

The potential energy between two atoms in a molecule is given by $U\left(x\right)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where $a$ and $b$ are $+$ve constants and $x$ is the distance between the atoms. The atom is in stable equilibrium when

A particle of mass m is projected with velocity v making an angle of ${45}^{\circ }$ with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where g = acceleration due to gravity)

Liquid rises to a height of $2\text{cm}$ in a capillary tube. The angle of contact between the solid and the liquid is zero. The tube is depressed more now so that the top of the capillary is only $1\text{cm}$ above the liquid. Then, the apparent angle of contact between the solid and the liquid is:

A monoatomic ideal gas is contained in a rigid container of volume $V$ with walls of total surface area $A$, thickness $x$ and thermal conductivity $K$. The gas is at an initial temperature $T_o$ and pressure $P_o$. The temperature of the surrounding air is $T_s$. All the temperatures are in absolute scale. If the temperature of the gas at any time $t$ can be expressed as $T\left(t\right)=T_s-(T_s-T_o)e^{-\lambda t}$, find the value of $\lambda$.

On observing light from three different stars P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximumin the spectrum of R and the intensity of red colour is maximum in the spectrum of Q. If $T_P,T_{Q}and{T}_R$ are the respective absolute temperatures of P, Q and R, then it can be concluded from the above observations that :

In one complete cycle, a heat engine extracts heat $Q_h$ from a thermal reservoir, does work W and does not eject any heat into the environment. This heat engine is impossible because its operation violates:

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10GHz$. What is the frequency of the microwave measured by the observer?

(speed of light $=3\times {10}^{8}m{s}^{-1}$)

In the figure a potential of 1200V is given to point A and point B is earthed, what is the potential at the point P?

An object at rest at the origin begins to move in the +x direction with a uniform acceleration of 1 m/s${}^2$ for 4 s and then it continues moving with a uniform velocity of 4 m/s in the same direction. The x - t graph for object's motion will be

An iron wire of length I is magnetized have a magnetic moment m. If it is bent inot a semicircle of radius r, its magnetic moment is

Carbon (Z = 6) with mass number 11 decays to boron (Z = 5). (a) Is it a ${\beta }^{+}$ -decay or a ${\beta }^{-}$ -decay? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90 $\%$ carbon - 11 and 10$\%$ boron - 11 (by the number of atoms ) converts itself into a mixture of 10$\%$ carbon - 11 and 90 $\%$ boron - 11 ?

The energy required to break a mercury drop of 1cm radius into 1000 small drops of equal size is….Joule (given the surface tension of mercury is $0.4N.m^{-1}$ )

All the curves in Column 1 are parabolic and those in Column 2 and Column 3 are straight lines.

‘x’, ‘v’ and ‘a’ denote position, velocity and acceleration of a particle and consider positive in the direction of increasing ‘x’.

Which one of the following options correctly represents a particle starting with positive position, positive velocity and uniform positive acceleration?

Length of the hour hand of a clock is $\frac{60}{\pi }\text{cm}$. Find the magnitude of average acceleration (in ${\text{rad/hr}}^2$) between the positions shown in the figure.