A network of four resistances is connected to \(9\,V\) battery, as shown in figure. The magnitude of voltage difference between the points \(A\) and \(B\) is .......... \(V.\)

A steel wire of length 2 m and Young's modulus \(2.0 \times 10^{11} \mathrm{Nm}^{-2}\) is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and \(10^{-3}\) respectively, then the elastic potential energy density of the wire is _______ \(\times 10^5\) (in SI units)

A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to

If \(\in\), \( E \) and \( t \) represent the free space permittivity, electric field and time respectively, then the unit of \( \frac{eE}{t} \) will be :

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range \(R\). If the time of flight of these bodies are \(5\) s and \(10\) s, respectively, then the value of \(R\) is ________ m. (Take \(g=10\) m/s\(^2\))

An alternating voltage \(\mathrm{V}(\mathrm{t})=220 \sin 100 \ \pi \mathrm{t}\) volt is applied to a purely resistive load of \(50\ \Omega\). The time taken for the current to rise from half of the peak value to the peak value is _______.

Given below are two statements: Statement \(I :\) An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement \(II :\) If \(R\) is the radius of a solid metallic sphere and \(Q\) be the total charge on it. The electric field at any point on the spherical surface of radius \(r ( < R )\) is zero but the electric flux passing through this closed spherical surface of radius \(r\) is not zero. In the light of the above statements, choose the correct answer from the options given below:

As shown in the figure, a bob of mass \(\mathrm{m}\) is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius \(\mathrm{r}\) and mass \(m\). When released from rest the bob starts falling vertically. When it has covered a distance of \(h\). the angular speed of the wheel will be

A \(10\, \Omega, 20 \; mH\) coil carrying constant current is connected to a battery of \(20 \; V\) through a switch is opened current becomes zero in \(100 \; \mu s\). The average emf induced in the coil is \(\dots \; V\).