Mass numbers of two nuclei are in the ratio of \(4: 3\). Their nuclear densities will be in the ratio of

A light beam is described by \(E=800 \sin \omega\left(t-\frac{x}{c}\right)\) An electron is allowed to move normal to the propagation of light beam with a speed of \(3 \times 10^{7}\;{ms}^{-1}\). What is the maximum magnetic force exerted on the electron ?

In the figure shown below, the charge on the left plate of the \(10\, \mu F\) capacitor is \(-30\,\mu C.\) The charge on the right place of the \(6\,\mu F\) capacitor is.....\(\mu C\)

A bi-convex lens has radius of curvature of both the surfaces same as \(1 / 6 \mathrm{~cm}\). If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides \(\left(R_1 \neq R_2\right)\), without any change in lens power then possible combination of \(R_1\) and \(R_2\) is :

A particle is moving in a straight line. The variation of position ' \(x\) ' as a function of time ' \(t\) ' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is _______.

An alternating voltage of amplitude \(40 \mathrm{~V}\) and frequency \(4 \mathrm{kHz}\) is applied directly across the capacitor of \(12 \mu \mathrm{F}\). The maximum displacement current between the plates of the capacitor is nearly _______.

Two wires \(A\) and \(B\) made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections \(3.0 \times 10^{-5} m^2\) and \(4.5 \times 10^{-5} m^2\), respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of \(A\) to that of \(B\) is \(x : 3\). The value of x is ___________.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is \(30 \;\mathrm{cm}\) and the refractive index of the lens material is \(1.5 .\) then the focal length of the lens (in \(\mathrm{cm}\) ) is

The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.

If an air bubble of diameter \(2\) mm rises steadily through a liquid of density \(2000\) kg/m\(^3\) at a rate of \(0.5\) cm/s, then the coefficient of viscosity of liquid is _______ Poise. (Take \(g = 10\) m/s\(^2\))

A thin convex lens \(L\) (refractive index \(= 1.5\)) is placed on a plane mirror \(M\). When a pin is placed at \(A\), such that \(OA = 18\, cm\), its real inverted image is formed at \(A\) itself, as shown in figure. When a liquid of refractive index \({\mu _1}\) is put between the lens and the mirror, the pin has to be moved to \(A’\). such that \(OA’ = 27\,cm\), to get its inverted real image at \(A'\) itself. The value of \({\mu _1}\) will be