The elongation of a wire on the surface of the earth is \(10^{-4} \; m\). The same wire of same dimensions is elongated by \(6 \times 10^{-5} \; m\) on another planet. The acceleration due to gravity on the planet will be \(\dots \; ms ^{-2}\). (Take acceleration due to gravity on the surface of earth \(=10 \; m / s ^{-2}\) )

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

A lamp emits monochromatic green light uniformly in all directions. The lamp is \(3\%\) efficient in converting electrical power to electromagnetic waves and consumes \(100\,W\) of power . The amplitude of the electric field associated with the electromagnetic radiation at a distance of \(5\,m\) from the lamp will be nearly.......\(V/m\)

A body travels \(102.5 \mathrm{~m}\) in \(\mathrm{n}^{\text {th }}\) second and \(115.0 \mathrm{~m}\) in \((n+2)^{\text {th }}\) second. The acceleration is what?

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 \mathrm{~km} / \mathrm{s}\), the root mean square velocity of oxygen at the same condition in \(\mathrm{km} / \mathrm{s}\) is _______.

An infinitely long straight wire carrying current \(I\) is bent in a planer shape as shown in the diagram. The radius of the circular part is r . The magnetic field at the centre O of the circular loop is :

Match List\(-I\) with List\(-II\).

List\(-I\)	List\(-II\)
\(A\). Gauss's Law in Electrostatics	\(I\). \(\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}\)
\(B\). Faraday's Law	\(II\). \(\oint \overrightarrow{ B } \cdot d \overrightarrow{ A }=0\)
\(C\). Gauss's Law in Magnetism	\(III\). \(\oint \vec{B} \cdot d \vec{l}=\mu_0 i_C+\mu_0 \in_0 \frac{d \phi_E}{d t}\)
\(D\). Ampere-Maxwell Law	\(IV\). \(\oint \overrightarrow{ E } \cdot d \overrightarrow{ s }=\frac{ q }{\epsilon_0}\)

Choose the correct answer from the options given below:

An experiment is performed to obtain the value of acceleration due to gravity \(g\) by using a simple pendulum of length \(L\). In this experiment time for \(100\, oscillations\) is measured by using a watch of \(1\, second\) least count and the value is \(90.0\, seconds\). The length \(L\) is measured by using a meter scale of least count \(1\, mm\) and the value is \(20.0\, cm\). The  error in the determination of \(g\) would be  ........... \(\%\)

Three charges +2q. +3q and -4q are situated at (0,-3a), (2a, 0) and (-2a,0) respectively in the xy plane. The resultant dipole moment about origin is _________

A mass \(M\) hangs on a massless rod of length \(l\) which rotates at a constant angular frequency. The mass \(M\) moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity \(\omega .\) The angular momentum of \(M\) about point \(A\) is \(L _{ A }\) which lies in the positive \(z\) direction and the angular momentum of \(M\) about \(B\) is \(L _{ B }\). The correct statement for this system is

A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi  \times {{10}^{ - 7}}\,N/{A^2}} \right)\)