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A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are ${\alpha }_C$ and ${\alpha }_B$ . On heating, the temperature of the strip goes up by DT and the strip bends to form an arc of radius of curvature R. Then R is

To an ideal non-linear triatomic gas, $800\text{cal}$ of heat energy is given at constant pressure. If vibrational modes are neglected, then the energy used by the gas in doing work against the surroundings is

An electric motor labelled 5KW is able to raise a load at speed of 25 m/s. Calculate the load being lifted.

Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel figure ?

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. Find the magnitude of the acceleration of the centre of mass of the two blocks.

How long will it take sound waves to travel the distance between the points A and B, separated by a distance l, if the air temperature between them varies linearly from $T_1$ to $T_2$? The velocity of sound propagation in air is equal to $v=\alpha \sqrt{T}$
Where $\alpha$ is a constant.

A filament bulb (500w , 100 v) is to be used in 230v main supply . When resistance R is connected in series , it works perfectly and the bulb consumes 500w . The value of R is.

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of the third orbit will be

A motor car starts from rest and accelerates uniformly for 10 seconds to a velocity of 40 m/s, it then runs at a constant speed and is finally brought to rest in 40 m with a constant acceleration.Total distance covered is 640 meters. Find acceleration, retardation and total time taken.

A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system

The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation, t = $\sqrt{x}$ + 3 where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is (given g = 10 $m{s}^{-2}$)

[Kerala (Engg.) 2000]

A current loop of area 0.01 m² and carrying a current of 10 amp is held perpendicular to magnetic field of induction of 0.1 tesla. The torque acting on the loop is

A body weighs $W_1$ in a liquid of density $d_1$ and $W_2$ in a liquid of density $d_2$. What is the weight in a liquid of density $d_3$?

A metal ball falls from a height of $1\text{m}$ on a steel plate and jumps upto a height of $81\text{cm}$. Find the coefficient of restitution for the collision.

A sphere of radius 1cm has potential of 8000 V ,then what will be energy density near its surface in J/m^3?

Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. the band gap in germanium is 0.65 eV.

Can you accelerate a particle at uniform speed. Explain

A particle is subjected to two SHMs $x_1=A_{1}sin\omega t$ and $x_2=A_2(\omega t+\frac{\pi }{4})$. The resultant SHM will have an amplitude of

Two equal spheres of mass $m$ are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Find the loss of K.E

Work done in converting one gram of ice at $-{10}^{\circ }\text{C}$ into steam at ${100}^{\circ }\text{C}$ is -
[Given, specific heat of ice $c_i=0.5{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$, specific heat of water $c_w=1{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$, latent heat of fusion of ice $L_f=80\text{cal/g}$, & latent heat of vaporization of steam $L_v=540\text{cal/g}$]

Evaluate : ${\int }_1^4(\frac{8}{\sqrt{t}}-12\sqrt{t^3})dt$

The ratio of the refractive index of red light to blue light in air is
[CPMT 1978]

A piston is fitted in a cylindrical tube of small cross section with the other end of the tube open. The tube resonates with a tuning fork of frequency 512 Hz. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of 32.0 cm. Calculate the speed of sound in the medium of the tube.

A cylinder of radius R is rolling with velocity of centre of mass $v=\frac{\omega R}{2}$ towards right. Keeping the centre of the cylinder as the origin, Find the coordinates of the point with zero net velocity.

When photons of energy $hv$ fall on an aluminium plate (work function $E_0)$, photoelectrons of maximum kinetic energy $K$ are ejected. If the frequency of radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be

A hollow cylinder is rolling without slipping on a horizontal surface as shown in figure. Then, the angular acceleration of the cylinder will be -

A particle of mass m is moving with a uniform speed v in x-y plane along a straight line, y = x + k, the angular momentum of the particle about the origin is

In simple harmonic motion, motion is executed by a particle that is subject to a force which is ___________to the displacement of the particle and is directed toward the______________.

A ring of mass $m$ and radius $R$ rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Find the velocity of transverse pulse in the ring.

A mass of $50\text{kg}$ is suspended from a spring of stiffness $10\text{kN/m}$. It is set into oscillations and it is observed that two successive oscillations have amplitudes $10\text{mm}$ and $1\text{mm}$. Determine the damping ratio.

1.1 - 0.03 = _________

Find derivative of $f\left(x\right)=e^{\cos x}+\ln x$

The maximum velocity of a harmonic oscillator is d and its maximum acceleration is $\beta$. Its time period will be

For the circuit shown in figure, match the following columns:

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \left(A\right)\text{Current in wire ae}& \left(p\right)1A\\ \left(B\right)\text{Current in wire be}& \left(q\right)2A\\ \left(C\right)\text{Current in wire ce}& \left(r\right)0.5A\\ \left(D\right)\text{Current in wire de}& \left(s\right)\text{none of these}\end{array}$

Find the value of $\theta$ in the diagram, so that the projectile can hit the target, placed at a height of $10m$ from ground (as shown). $(g=10{\text{m/s}}^2$)

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures $t_1$ and $t_2$ of the liquid, fractions $f_1$ and $f_2$ of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

A crane is pushing a car of mass 100 kg with a constant acceleration of $2m/s^2$ on a horizontal smooth road. Find the force that the crane applies on the car?

If the heat of $110\text{J}$ is added to a gaseous system and it acquires internal energy of $40\text{J}$, then the amount of internal work done is

A thin uniform rod of length $L$ and mass $M$ is bent at length ratio $1:2$ such that the angle between them is ${90}^{\circ }$. The moment of inertia of the bent rod about an axis passes through the bending point and perpendicular to the plane is

If $M$ is the mass of water that rises in a capillary tube of radius $r$, then mass of water which will rise in a capillary tube (of same material) of radius $2r$ is

If a fluid having viscosity $0.6{\text{Ns/m}}^2$ and density of $900{\text{kg/m}}^3$, flows through a pipe of diameter $40\text{mm}$, then find the maximum velocity of fluid (in $\text{m/s}$) inside the pipe for laminar flow. (Critical Reynold's number $=2100$)

A microwave oven rotates with angular speed $2\omega$ and initial frequency $f_i$. If angular speed decreases to $\omega$, final frequency $f_f$ of the rotor is