For a transistor to act as a switch, it must be operated in

Two planets have masses \(M\) and \(16\, M\) and their radii are \(a\) and \(2\, a\) respectively. The separation between the centres of the planets is \(10\, a.\) A body of mass \(m\) is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is

The magnetic field existing in a region is given by \(\overrightarrow{\mathrm{B}}=0.2(1+2 \mathrm{x}) \hat{\mathrm{k} T}\). A square loop of edge \(50 \mathrm{~cm}\) carrying \(0.5 \mathrm{~A}\) current is placed in \(x-y\) plane with its edges parallel to the \(x-y\) axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is___________ \(\mathrm{mN}\).

When a rubber-band is stretched by a distance \(x\), it exerts restoring force of magnitude  \(F=ax+bx^2\) where \(a\) and \(b\) areconstants. The work done in stretching the unstretched rubber-band by \(L\) is

A transparent block A having refractive index \(\mu=1.25\) is surrounded by another medium of refractive index \(\mu=1.0\) as shown in figure. A light ray is incident on the flat face of the block with incident angle \(\theta\) as shown in figure. What is the maximum value of \(\theta\) for which light suffers total internal reflection at the top surface of the block?

The angle of projection for a projectile to have same horizontal range and maximum height is _______.

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of \(3\,s\) and \(4\,s\) respectively. If their moments of inertia are in the ratio of \(3: 2\) then the ratio of their magnetic moments will e.

A cylinder with fixed capacity of \(67.2\, lit\) contains helium gas at \(STP\). The amount of heat needed to raise the temperature of the gas by \(20\,^oC\) is ..... \(J\) [Given that \(R = 8.31\, J\, mol^{-1}\, K^{-1}\)]

A parallel plate capacitor with width \(4\,cm\), length \(8\,cm\) and separation between the plates of \(4\,mm\) is connected to a battery of \(20\,V\). A dielectric slab of dielectric constant \(5\) having length \(1\,cm\), width \(4\,cm\) and thickness \(4\,mm\) is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be......... \(\in_{0}\,J\). (Where \(\epsilon_{0}\) is the permittivity of free space)

If the initial velocity in horizontal direction of a projectile is unit vector \(\hat{i}\) and the equation of trajectory is \(y =5 x (1- x )\). The \(y\) component vector of the initial velocity is. (Take \(g=10\,m / s ^{2}\) )

Young’s moduli of two wires \(A\) and \(B\) are in the ratio \(7 : 4\). Wire \(A\) is \(2\, m\) long and has radius \(R\). Wire \(A\) is \(2\, m\) long and has radius \(R\). Wire \(B\) is \(1.5\, m\) long and has radius \(2\, mm\). If the two wires stretch by the same length for a given load, then the value of \(R\) is close to ......... \(mm\)

The mid points of two small magnetic dipoles of length \(d\) in end-on positions, are separated by a distance \(x, (x > > d)\). The force between them is proportional to \(x^{-n}\) where \(n\) is

From a sphere of mass \(M\) and radius \(R\), a smaller sphere of radius \(\frac{R}{2}\) is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure) . For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is \(3R\), the gravitational force between the two sphere is