A parallel beam of light is allowed to fall on a transparent spherical globe of diameter \(30 \,cm\) and refractive index \(1.5\). The distance from the centre of the globe at which the beam of light can converge is________ \(mm\)

A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are :

The figure shows a square loop \(L\) of side \(5\, cm\) which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of \(1\, cms^{-1}\). At some instant, a part of \(L\) is in a uniform magnetic field of \(1\, T\), perpendicular to the plane of the loop. If the resistance of \(L\) is \(1.7\,\Omega \), the current in the loop at that instant will be close to.....\(\mu A\)

A freshly prepared radioactive source of half life \(2\) hours \(30\) minutes emits radiation which is \(64\) times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

An aluminium wire is stretched to make its length, \(0.4 \,\%\) larger. Then percentage change in resistance is \(.....\,\%\)

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its werght on the surface of earth is \(200\,N\), will be \(...........\,N\) ( \(Given R =\) Radrus of earth)

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively \(\left( k _{\text {sph }}: k _{ cyl }\right)\) is \(2: \sqrt{ x }\), then value of \(x\) is .............

The motion of a mass on a spring, with spring constant \({K}\) is as shown in figure. The equation of motion is given by \(x(t)= A sin \omega t+ Bcos\omega t\) with \(\omega=\sqrt{\frac{K}{m}}\) Suppose that at time \(t=0\), the position of mass is \(x(0)\) and velocity \(v(0)\), then its displacement can also be represented as \(x(t)=C \cos (\omega t-\phi)\), where \(C\) and \(\phi\) are

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should by unbinding the strings to achieve a speed of \(4\,ms ^{-1}\), is\(........cm\). \(\left(\right.\) take \(\left.g=10\,ms ^{-2}\right)\)

In the given figure, the charge stored in \(6 \ \mu \mathrm{F}\) capacitor, when points \(A\) and \(B\) are joined by a connecting wire is _______ \(\mu \mathrm{C}\).

The focal length \(f\) is related to the radius of curvature \(R\) of the spherical convex mirror by