A metal block of mass \(m\) is suspended from a rigid support through a metal wire of diameter \(14\,mm\). The tensile stress developed in the wire under equilibrium state is \(7 \times 10^5\,Nm ^{-2}\). The value of mass \(m\) is \(......kg\). (Take, \(g =9.8\,ms ^{-2}\) and \(\left.\pi=\frac{22}{7}\right)\)

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle \(45^{\circ}\) with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is:

Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below 

In thermodynamics, heat and work are

Two massless springs with spring constants \(2\,k\) and \(9\,k\), carry \(50\, g\) and \(100 \,g\) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is

A thermodynamic system is taken from an original state \(D\) to an intermediate state \(E\) by the linear process shown in the figure. Its volume is then reduced to the original volume from \(E\) to \(F\) by an isobaric process. The total work done by the gas from \(D\) to \(E\) to \(F\) will be \(......J\)

Two conductors have the same resistances at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \(\alpha_1\) and \(\alpha_2\). The respective temperature coefficients for their series and parallel combinations are _______.

If \(a,\, b,\,c,\,d\) are inputs to a gate and \(x\) is its output, then, as per the following time graph, the gate is

The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\  \mu \mathrm{F}\))

A magnet of total magnetic moment \({10\,^{ - 2}}\hat i\,A - {m^2}\) is placed in a time varying magnetic field, \(B\,\hat i\,\left( {\cos \,\omega t} \right)\) where \(B = 1\, Tesla\) and \(\omega  = 0.125\, rad/s\). The work done for reversing the direction of the magnetic moment at \(t = 1\, second\), is