Consider a uniform cubical box of side \(a\) on a rough floor that is to be moved by applying minimum possible force \(F\) at a point \(b\) above its centre of mass (see figure). If the coefficient of friction is \(\mu=0.4,\) the maximum possible value of \(100 \times \frac{b}{a}\) for a box not to topple before moving is

A moving coil galvanometer allows a full scale current of \(10^{-4}\, A\). A series resistance of \(2\, M\,\Omega \) is required to convert the above galvanometer into a voltmeter of range \(0 -5\, V\). Therefore the value of shunt resistance required to convert the above galvanometer into a ammeter of range \(0-10\, mA\) is....\(\Omega \)

A system of three polarizers \(P_1, P_2, P_3\) is set up such that the pass axis of \(P_3\) is crossed with respect to that of \(P_1\). The pass axis of \(P_2\) is inclined at \(60^o\) to the pass axis of \(P_3\). When a beam of unpolarized light of intensity \(I_0\) is incident on \(P_1\), the intensity of light transmitted by the three polarizers is \(I\). The ratio \((I_0/I)\) equals (nearly)

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of \(2 \,\Omega\). The value of internal resistance of each cell is ............ \(\Omega\)

Two satellites \(A\) and \(B\) move round the earth in the same orbit. The mass of \(A\) is twice the mass of \(B\). The quantity which is same for the two satellites will be :

The electric field of a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos (\mathrm{kz}+\omega \mathrm{t})\) At \(\mathrm{t}=0,\) a positively charged particle is at the point \((\mathrm{x}, \mathrm{y}, \mathrm{z})=\left(0,0, \frac{\pi}{\mathrm{k}}\right) .\) If its instantaneous velocity at \((t=0)\) is \(v_{0} \hat{\mathrm{k}},\) the force acting on it due to the wave is

A simple pendulum oscillating in air has period \(T.\) The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is \(\frac {1}{16}\) of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is

A freshly prepared radioactive source of half life \(2\) hours \(30\) minutes emits radiation which is \(64\) times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is \(\frac{\alpha}{10}\). The value of \(\alpha\) is _________

A force \(F=\left(5+3 y^2\right)\) acts on a particle in the \(y\) direction, where \(F\) is newton and \(y\) is in meter. The work done by the force during a displacement from \(y =2\,m\) to \(y =5\,m\) is \(.............\,j\).

Consider two \(npn\) transistors as shown in figure. If \(0\,Volts\) corresponds to false and \(5\, Volts\) correspond to true then the output at \(C\) corresponds to