A constant Power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time \('t'\) is proportional to

The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is  (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\)

If a body of mass \(1\) kg falls on the earth from infinity, it attains velocity \((v)\) and kinetic energy \((k)\) on reaching the surface of earth. The values of \(v\) and \(k\) respectively are _______. (Take radius of earth to be \(6400\) km and \(g = 9.8\) m/s\(^2\))

The galvanometer deflection, when key \(K_1\) is closed but \(K_2\) is open, equals \(\theta_0\) (see figure). On closing \(K_2\) also and adjusting \(R_2\) to \(5\,\Omega \) , the deflection in galvanometer becomes \(\frac{{\theta _0}}{5}\). The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: .................. \(\Omega\)

The magnetic field in a travelling electromagnetic wave has a peak value of \(20\ n T\). The peak value of electric field strength is......\(Vm^{-1}\)

A system consists of two types of gas molecules \(A\) and \(B\) having same number density \(2 \times\) \(10^{25}\, / {m}^{3}\). The diameter of \({A}\) and \({B}\) are \(10\, \stackrel{\circ}{{A}}\) and \(5\, \stackrel{\circ}{{A}}\) respectively. They suffer collision at room temperature. The ratio of average distance covererd by the molecule \(A\) to that of \(B\) between two successive collision is \(.....\,\times 10^{-2}\)

A long straight wire of radius ' \(a\) ' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at \(\frac{a}{2}\) and \(2\)a from axis of the wire is _______.

A light wave is incident normally on a glass slab of refractive index \(1.5\). If \(4\%\) of light gets reflected and the amplitude of the electric field of the incident light is \(30\, V/m\), then the amplitude of the electric field for the wave propagating in the glass medium will be.......\( V/m\)

A vector \(\vec A \) is rotated by a small angle \(\Delta \theta\) radian \(( \Delta \theta << 1)\) to get a new vector \(\vec B\) In that case \(\left| {\vec B - \vec A} \right|\) is

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between \(A\) and \(B\) is \(.......\Omega\).

Due to presence of an em-wave whose electric component is given by \(\mathrm{E}=100 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}\), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

A particle of mass \('{m}'\) is moving in time \('t'\) on a trajectory given by \(\overrightarrow{{r}}=10 \alpha {t}^{2}\, \hat{{i}}+5 \beta({t}-5)\, \hat{{j}}\) Where \(\alpha\) and \(\beta\) are dimensional constants. The angular momentum of the particle becomes the same as it was for \({t}=0\) at time \({t}=\) .....\(seconds.\)

An astronaut of mass \(m\) is working on a satellite or biting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_G\) on the astronaut is