Imagine that a reactor converts all given mass into energy and that it operates at a power level of \(10^9\, watt\). The mass of the fuel consumed per hour in the reactor will be : (velocity of light, \(c\) is \(3\times10^8\, m/s\))

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is ___________ mV.

Two planets, \(A\) and \(B\) are orbiting a common star in circular orbits of radius \(R_A\) and \(R_B\), respectively, with \(R_B=2 R_A\). The planet \(B\) is \(4 \sqrt{2}\) times more massive than planet \(A\). The ratio \(\left(\frac{L_B}{L_A}\right)\) of angular momentum \(\left(L_B\right)\) of planet \(B\) to that of planet \(A\left(L_A\right)\) is closest to integer ________.

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:

A \(0.4\,kg\) mass takes \(8 s\) to reach ground when dropped from a certain height ' \(P\) ' above surface of earth. The loss of potential energy in the last second of fall is \(..............J\). [Take \(g =10\,m / s ^2\) ]

Two identical small bar magnets each of dipole moment \(3\sqrt{5}\) J/T are placed at a center to center separation of \(10\) cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is \(\alpha \times 10^{-3}\) T. The value of \(\alpha\) is ______.
(\(\mu_0=4\pi \times 10^{-7}\) Tm/A)

A coil of \(200\) turns and area \(0.20 \mathrm{~m}^2\) is rotated at half a revolution per second and is placed in uniform magnetic field of \(0.01 \mathrm{~T}\) perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \(\frac{2 \pi}{\beta}\) volt. The value of \(\beta\) is _______.

\({T}_{0}\) is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \(\frac{1}{16}\) times of its initial value, the modified time

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is _______.

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :

A block of mass \(M\) placed inside a box descends vertically with acceleration \('a'\). The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of \('a'\) will be .............

A uniform magnetic field \(B\) exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of \(4\, mm\) and a total length of \(30\, cm\) The magnetic field changes with time at a steady rate \(dB / dt =0.032\, Ts ^{-1} .\) The induced current in the \(100 p\) is close to \(....A\) (Resistivity of the metal wire is \(\left.1.23 \times 10^{-8}\, \Omega m \right)\)

A uniform cylinder of mass \(M\) and radius \(R\) is to be pulled over a step of height \(a (a < R\)) by applying a force \(F\) at its centre \('O'\) perpendicular to the plane through the axes of the cylinder on the edge of the step ( see figure). The minimum value of \(F\) required is