\({T}_{0}\) is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \(\frac{1}{16}\) times of its initial value, the modified time

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as  \({}_{92}{U^{235}} + {}_0{n^1} \to {}_{56}B{a^{141}} + {}_{36}K{r^{92}} + 3x + Q{\rm{( energy)}}\) where three particles named \(x\) are produced and energy \(Q\) is released. What is the name of the particle \(x\) ?

When UV light of wavelength \(300 \mathrm{~nm}\) is incident on the metal surface having work function \(2.13 \mathrm{eV}\), electron emission takes place. The stopping potential is _______. (Given hc \(=1240 \mathrm{eV} \mathrm{nm}\) )

In the given circuit of potentiometer, the potential difference \(E\) across \(AB\) ( \(10\, m\) length) is larger than \(E _{1}\) and \(E _{2}\) as well. For key \(K _{1}\) (closed), the jockey is adjusted to touch the wire at point \(J_{1}\) so that there is no deflection in the galvanometer. Now the first battery \(\left( E _{1}\right)\) is replaced by second battery \(\left( E _{2}\right)\) for working by making \(K _{1}\) open and \(K _{2}\) closed. The galvanometer gives then null deflection at \(J _{2}\). The value of \(\frac{ E _{1}}{ E _{2}}\) is \(\frac{ a }{ b },\) where \(a =\) ...............

The truth table for the followng logic circuit is ...... .

\(27\) similar drops of mercury are maintained at \(10 \,V\) each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop.

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be:

A 2 A current carrying straight metal wire of resistance \(1 \Omega\), resistivity \(2 \times 10^{-6} \Omega m\), area of cross-section \(10 mm^2\) and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field \(\vec{B}\). The magnitude of \(B\) is _______ \(\times 10^{-1} T\) (given, \(g =10 m / s ^2\) ).

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about \(150\, N/C\), directed inward towards the center of the Earth . This gives the total net surface charge carried by the Earth to be......\(kC\) [Given \({\varepsilon _0} = 8.85 \times {10^{ - 12}}\,{C^2}/N - {m^2},{R_E} = 6.37 \times {10^6}\,m\)]

A monkey of mass \(50\,kg\) climbs on a rope which can withstand the tension \((T)\) of \(350\,N\). If monkey initially climbs down with an acceleration of \(4\,m / s ^{2}\) and then climbs up with an acceleration of \(5\,m / s ^{2}\). Choose the correct option \(\left( g =10\,m / s ^{2}\right)\)

A uniform rod \(AB\) is suspended from a point \(X\), at a variable distance from \(x\) from \(A\), as shown. To make the rod horizontal, a mass \(m\) is suspended from its end \(A\). A set of \((m, x)\) values is recorded. The appropriate variable that give a straight line, when plotted, are

A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\;ms^{-1}\) at a point where the pressure is \(P\) Pascal. At another point where pressure is \(\frac{ P }{2}\) Pascal its speed is \(V\;ms^{-1}\). If the density of the fluid is \(\rho\, kg\, m ^{-3}\) and the flow is streamline, then \(V\) is equal to