A positive charge particle of \(100 \,mg\) is thrown in opposite direction to a uniform electric field of strength \(1 \times 10^{5} \,NC ^{-1}\). If the charge on the particle is \(40 \,\mu C\) and the initial velocity is \(200 \,ms ^{-1}\), how much distance (in \(m\)) it will travel before coming to the rest momentarily

A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be 

Match list-\(I\) with list-\(II\):

List-\(I\)	List-\(II\)
\((A)\)Kinetic energy of plant	\((I)\) \(-\frac{\mathrm{GMm}}{\mathrm{a}}\)
\((B)\) Gravaitatioin potentiyal energy of sun -plant system	\((II)\) \(\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
\((C)\)Total mecaniacal energy of palnt	\((III)\) \(\frac{\mathrm{Gm}}{\mathrm{r}}\)
\((D)\)Escap energyat the surface of plant for unit mass object	\((IV)\) \(-\frac{\mathrm{GMm}}{2 \mathrm{a}}\)

(Where \(\mathrm{a}=\) radius of planet orbit, \(\mathrm{r}=\) radius of planet, \(M=\) mass of Sun, \(m=\) mass of planet)
Choose the correct answer from the options given below:

A square loop of area \(25\,cm ^2\) has a resistance of \(10\,\Omega\). The loop is placed in uniform magnetic field of magnitude \(40.0 T\). The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in \(1.0 sec\), will be \(..........\times 10^{-3}\)

The time period of a satellite, revolving above earth's surface at a height equal to \(R\) will be (Given \(g =\pi^2 m / s ^2, R =\) radius of earth)

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

List\(-I\)	List\(-II\)
\((a)\) Magnetic Induction	\((i)\) \({ML}^{2} {T}^{-2} {A}^{-1}\)
\((b)\) Magnetic Flux	\((ii)\) \({M}^{0} {L}^{-1} {A}\)
\((c)\) Magnetic Permeability	\((iii)\) \({MT}^{-2} {A}^{-1}\)
\((d)\) Magnetization	\((iv)\) \({MLT}^{-2} {A}^{-2}\)

Choose the most appropriate answer from the options given below:

A uniform rod of length \('l'\) is pivoted at one of its ends on a vertical shaft of negligible radius When the shaft rotates at angular speed \(\omega\) the rod makes an angle \(\theta\) with it (see figure). To find \(\theta\) equate the rate of change of angular momentum (direction going into the paper ) \(\frac{ m \ell^{2}}{12} \omega^{2} \sin \theta \cos \theta\) about the centre of mass \((CM)\) to the torque provided by the horizontal and vertical forces \(F_{H}\) and \(F_{V}\) about the CM. The value of \(\theta\) is then such that:

A certain pressure \(P\) is applied to \(1\) litre of water and \(2\) litre of a liquid separately. Water gets compressed to \(0.01 \%\) whereas the liquid gets compressed to \(0.03 \%\). The ratio of Bulk modulus of water to that of the liquid is \(\frac{3}{x}\). The value of \(x\) is \(...........\)

A hydrogen atom in is ground state absorbs \(10.2\;eV\) of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ............... \(\times 10^{-34} \; J {s}\) (Given, Plank's constant \(\left.=6.6 \times 10^{-34} Js \right)\)

An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is: __________ .

Three blocks \(A\), \(B\) and \(C\) are pulled on a horizontal smooth surface by a force of \(80 \mathrm{~N}\) as shown in figure. The tensions \(T_1\) and \(T_2\) in the string are respectively _______ and _______.