Figure shows a part of an electric circuit. The potentials at points \(a , b\) and \(c\) are \(30\,V , 12\,V\) and \(2\,V\) respectively. The current through the \(20 \Omega\) resistor will be \(........\,A\)

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 .............

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of \(8 \mathrm{~A} / \mathrm{s}\). At an instant when R is \(12 \Omega\), the value of the current in the circuit will be ______ A.

Four particles \(A, B, C, D\) of mass \(\frac{\mathrm{m}}{2}, \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}\), have same momentum, respectively. The particle with maximum kinetic energy is _______.

A quantity \(f\) is given by \(f=\sqrt{\frac{{hc}^{5}}{{G}}}\) where \(c\) is speed of light, \(G\) universal gravitational constant and \(h\) is the Planck's constant. Dimension of \(f\) is that of

In case of vertical circular motion of a particle by a thread of length \(r\) if the tension in the thread is zero at an angle \(30^{\circ}\) shown in figure, the velocity at the bottom point (A) of the circular path is ( \(g =\) gravitational acceleration)

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 ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees.

A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)

Work done by a Carnot engine operating between temperatures \(127^{\circ}\,C\) and \(27^{\circ}\,C\) is \(2\,kJ\). The amount of heat transferred to the engine by the reservoir is \(........\,kJ\)

A unit scale is to be prepared whose length does not change with temperature and remains \(20\,cm\), using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is \(40\,cm\) and length of iron will be\(...cm\) \(\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.\) and \(\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)\).