A Carnot engine, having an efficiency of $$\eta =1/10$$ as heat engine, is used as a refrigerator . If the work done on the system is $$10$$ $$J$$, the amount of energy absorbed from the reservoir at lower temperature is

An electric charge $$10^{-3}\mu C$$ is placed at the origin $$(0,0)$$ of $$X-Y$$ co-ordinate system. Two points $$A$$ and $$B$$ are situated at $$\left(\sqrt{2},\sqrt{2}\right)$$ and $$\left(2,0\right)$$ respectively. The potential difference between the points $$A$$ and $$B$$ will be

Charges are placed on the vertices of a square as shown. Let $$\overrightarrow{E}$$ be the electric field and $$V$$ the potential at the center. If the charges on $$A$$ and $$B$$ are interchanged with those on $$D$$ and $$C$$ respectively, then

The potential at a point $$x$$ (measured in $$\mu m$$) due to some charges situated on the $$x$$-axis is given by $$V\left(x\right)=20/\left(x^2-4\right)$$ volt The electric field $$E$$ at $$x=4\mu m$$ is given by

The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

Photon of frequency $$v$$ has a momentum associated with it. If $$c$$ is the velocity of light, the momentum is

If $$g_E$$ and $$g_M$$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio {{electro\,\,ch\arg e\,\,on\,\,the\,\,moon} \over {electronic\,\,ch\arg e\,\,on\,\,the\,\,earth}}\,\,to\,be

In a Young's double slit experiment the intensity at a point where the path difference is {\lambda \over 6} ( $$\lambda$$ being the wavelength of light used ) is $$I$$. If $$I_0$$ denotes the maximum intensity, {I \over {{I_0}}} is equal to

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

A parallel plate condenser with a dielectric of dielectric constant $$K$$ between the plates has a capacity $$C$$ and is charged to a potential $$V$$ volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

A sound absorber attenuates the sound level by $$20$$ $$dB$$. The intensity decreases by a factor of

A charged particle with charge $$q$$ enters a region of constant, uniform and mutually orthogonal fields $$\overrightarrow{E}$$ and $$\overrightarrow{B}$$ with a velocity $$\overrightarrow{v}$$ perpendicular to both $$\overrightarrow{E}$$ and $$\overrightarrow{B},$$ and comes out without any change in magnitude or direction of $$\overrightarrow{v}$$. Then

A charged particle moves through a magnetic field perpendicular to its direction. Then

A current $$I$$ flows along the length of an infinitely long, straight, thin walled pipe. Then

A long straight wire of radius $$a$$ carries a steady current $$i.$$ The current is uniformly distributed across its cross section. The ratio of the magnetic field at $$a/2$$ and $$2a$$ is

Two identical conducting wires $$AOB$$ and $$COD$$ are placed at right angles to each other. The wire $$AOB$$ carries an electric current $$I_1$$ and $$COD$$ carries a current $$I_2$$. The magnetic field on a point lying at a distance $$d$$ from $$O$$, in a direction perpendicular to the plane of the wires $$AOB$$ and $$COD$$ , will be given by

A block of mass $$m$$ is connected to another block of $$mass$$ $$M$$ by a spring (massless) of spring constant $$k.$$ The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $$F$$ starts acting on the block of mass $$M$$ to pull it. Find the force of the block of mass $$m.$$

An ideal coil of $$10H$$ is connected in series with a resistance of $$5\Omega$$ and a battery of $$5V$$. $$2$$ second after the connection is made, the current flowing in ampere in the circuit is

A round uniform body of radius $$R,$$ mass $$M$$ and moment of inertia $$I$$ rolls down (without slipping) an inclined plane making an angle $$\theta$$ with the horizontal. Then its acceleration is

Angular momentum of the particle rotating with a central force is constant due to