The disintegration energy \(Q\) for the nuclear fission of \({ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+\mathrm{n}\) is _______ \(\mathrm{MeV}\). Given atomic masses of \({ }^{235} \mathrm{U}: 235.0439 \mathrm{u},{ }^{140} \mathrm{Ce} ; 139.9054 \mathrm{u},\) \({ }^{94} \mathrm{Zr}: 93.9063 \mathrm{u} ; \mathrm{n}: 1.0086 \mathrm{u},\) Given Value of \(\mathrm{c}^2=931 \mathrm{MeV} / \mathrm{u}\)

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is \((A)\) directly proportional to the length of the potentiometer wire \((B)\) directly proportional to the potential gradient of the wire \((C)\) inversely proportional to the potential gradient of the wire \((D)\) inversely proportional to the length of the potentiometer wire Choose the correct option for the above statements:

The number density of free electrons in copper is nearly \(8 \times 10^{28}\,m ^{-3} . A\) copper wire has its area of cross section \(=2 \times 10^{-6}\,m ^2\) and is carrying a current of \(3.2\,A\). The drift speed of the electrons is \(.....\times 10^{-6}\,ms ^{-1}\).

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of \(0.8 \mathrm{~cm}^3\). If the bulk modulus of the liquid is 2 GPa , the initial volume of the liquid was _______ litre. \(\left(\right.\) Take \(\left.1 \mathrm{~atm}=10^5 \mathrm{~Pa}\right)\)

Seawater at a frequency \(f =9 \times 10^{2} \,Hz ,\) has permittivity \(\varepsilon=80\, \varepsilon_{0}\) and resistivity \(\rho=0.25\, \Omega m.\) Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source \(V ( t )= V _{0} \sin (2 \pi ft ) .\) Then the conduction current density becomes \(10^{x}\) times the displacement current density after time \(t =\frac{1}{800} \,s\). The value of \(x\) is ......... .
\(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right)\)

The potential energy of a particle changes with distance \(x\) from a fixed origin as \(V = \dfrac{A\sqrt{x}}{x + B}\), where \(A\) and \(B\) are constant with appropriate dimensions. The dimensions of \(AB\) are _______.

A body is moving in a low circular orbit about a planet of mass \(M\) and radius \(R\). The radius of the orbit can be taken to be \(R\) it self. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is

A metal rod of length \(L\) rotates about one end at origin with a uniform angular velocity \(\omega\). The magnetic field radially falls off as \(B(r) = B_0 e^{-\lambda r}\); \(\lambda\) being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

\(UV\) light of \(4.13 \mathrm{eV}\) is incident on a photosensitive metal surface having work function \(3.13 \mathrm{eV}\). The maximum kinetic energy of ejected photoelectrons will be _______.

To increase the resonant frequency in series \(LCR\) circuit,

The aperture diameter of a telescope is \(5\; \mathrm{m} .\) The separation between the moon and the earth is \(4 \times 10^{5} \;\mathrm{km} .\) With light of wavelength of \(5500\;\mathring A\), the minimum separation between objects on the surface of moon, so that they are just resolved, is close to......\(m\)

The balancing length for a cell is \(560 \;\mathrm{cm}\) in a potentiometer experiment. When an external resistance of \(10 \;\Omega\) is connected in parallel to the cell, the balancing length changes by \(60\; \mathrm{cm} .\) If the internal resistance of the cell is \(\frac{\mathrm{N}}{10} \;\Omega,\) where \(\mathrm{N}\) is an integer then value of \(\mathrm{N}\) is

Seven identical circular planar disks, each of mass \(M\) and radius \(R\) are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point \(P\) is: