A radioactive sample disintegrates via two independent decay processes having half lives \(T _{1 / 2}^{(1)}\) and \(T _{1 / 2}^{(2)}\) respectively. The effective half- life \(T _{1 / 2}\) of the nuclei is

A wire of resistance \(R_{1}\) is drawn out so that its length is increased by twice of its original length.The ratio of new resistance to original resistance is.

Light is incident from a medium into air at two possible angles of incidence \((A)\, 20^o\) and \((B)\, 40^o\) . In the medium light travels \(3.0\, cm\) in \(0.2\, ns\). The ray will

In a meter bridge experiment the balance point in obtained if the gaps are closed by \(2\,\Omega\) and \(3\,\Omega\). A shunt of \(x\,\Omega\) is added to \(3\,\Omega\) resistor to shift the balancing point by \(22.5\,cm\). The value of \(X\) is \(................\)

The time period of a satellite in a circular orbit of radius \(R\) is \(T\). The period of another satellite in a circular orbit of radius \(9 R\) is............ \(T\)

Match List \(- I\) (Fundamental Experiment) with List \(- II\) (its conclusion) and select the correct option from the choices given below the list \(\begin{array}{|||} \hline List\,\,-1  & List\,\,-II\,\,  \\ \hline a\,\,Franck-Hertz\,\,Experiment & i\,\,Particle\,\,nature\,\,of\,\,light \\ \hline b\,\,Photo\,\,-electric\,\,Experiment & ii\,\,Discrete\,\,energy \,\, levels\,\,of\,\,atom \\ \hline c\,\,Davison-Germer\,\,Experiment & iii\,\,Wave\,\,nature\,\,of\,\,electron \\ \hline  & iv\,\,Structure\,\,of\,\,atom  \\ \hline \end{array}\)

Two cars A and B each of mass \(10^3 kg\) are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds \(72 km / h\) and \(36 km / h\). The magnitude of angular momentum of car \(A\) with respect to car \(B\) is _________ J.s.

A coil having \(100\) turns, area of \(5 \times 10^{-3} \mathrm{~m}^2\), carrying current of \(1 \mathrm{~mA}\) is placed in uniform magnetic field of \(0.20 \mathrm{~T}\) such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through \(90^{\circ}\) is _______ \(\mu \mathrm{J}\).

A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\)  \((g\, = 10\, m\,s^{-2})\)

A series \(LCR\) circuit consists of \(R =80\,\Omega X _{ L }=100\, \Omega\) and \(X _{ C }=40\, \Omega\) The input voltage is \(2500 \cos (100 \pi t )\,V\). The amplitude of current, in the circuit, is \(................A.\)

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :