A convex lens of focal length \(40 \mathrm{~cm}\) forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length \(20 \mathrm{~cm}\). The photoelectric current now is:

A body of mass \(m\) is moving in a circular orbit of radius \(R\) about a planet of mass \(M\). At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \(\frac{R}{2}\) , and the other mass, in a circular orbit of radius \(\frac{3R}{2}\). The difference between the final and initial total energies is

Consider a sphere of radius \(\mathrm{R}\) which carries a uniform charge density \(\rho .\) If a sphere of radius \(\frac{\mathrm{R}}{2}\) is carved out of it, as shown, the ratio \(\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}\) of magnitude of electric field \(\overrightarrow{\mathrm{E}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{E}}_{\mathrm{B}}\) respectively, at points \(\mathrm{A}\) and \(\mathrm{B}\) due to the remaining portion is

Which one is the correct option for the two different thermodynamic processes ?

A block of mass \(m\) is placed on a surface having vertical cross section given by \(y=x^2 / 4\). If coefficient of friction is \(0.5\) , the maximum height above the ground at which block can be placed without slipping is _______.

A copper ball of radius \(1\, cm\) and work function \(4.47\,eV\) is irradiated with ultraviolet radiation of wavelength \(2500\mathop A\limits^o \). The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is

A heavy box of mass \(50 \mathrm{~kg}\) is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is \(0.3\) then force of kinetic friction is _______.

Average force exerted on a non-reflecting surface at normal incidence is \(2.4 \times 10^{-4} \mathrm{~N}\). If \(360 \mathrm{~W} / \mathrm{cm}^2\) is the light energy flux during span of \(1\) hour \(30\) minutes. Then the area of the surface is _______.

A charge particle of \(2\,\mu\,C\) accelerated by a potential difference of \(100\,V\) enters a region of uniform magnetic field of magnitude \(4\,m\,T\) at right angle to the direction of field. The charge particle completes semicircle of radius \(3\,cm\) inside magnetic field. The mass of the charge particle is \(........\times 10^{-18}\,kg\).

\(B _{ X }\) and \(B _{ Y }\) are the magnetic field at the centre of two coils of two coils \(X\) and \(Y\) respectively, each carrying equal current. If coil \(X\) has \(200\) turns and \(20 cm\) radius and coil \(Y\) has \(400\) turns and \(20 cm\) radius, the ratio of \(B _{ X }\) and \(B _{ Y }\) is