An object of mass \(m _{1}\) collides with another object of mass \(m _{2}\), which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses \(m _{2}: m _{1}\) is

A ray of light \(AO\) in vacuum is incident on a glass slab at angle \(60^o\) and refracted at angle \(30^o\) along \(OB\) as shown in the figure. The optical path length of light ray from \(A\) to \(B\) is

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

List \(I\)	List \(II\)
\((a)\) Rectifier	\((i)\) Used either for stepping up or stepping down the \(a.c.\) voltage
\((b)\) Stabilizer	\((ii)\) Used to convert \(a.c.\) voltage into \(d.c.\) voltage
\((c)\) Transformer	\((iii)\) Used to remove any ripple in the rectified output voltage
\((d)\) Filter	\((iv)\) Used for constant output voltage even when the input voltage or load current change

Choose the correct answer from the options given below:

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

\(Sl\). \(No\).	\(R\, (\Omega )\)	\(l\, (cm)\)
\(1\).	\(1000\)	\(60\)
\(2\).	\(100\)	\(13\)
\(3\).	\(10\)	\(1.5\)
\(4\).	\(1\)	\(1.0\)

Which of the readings is inconsistent ?

A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

The energy released per fission of nucleus of \({ }^{240} X\) is \(200 MeV\). The energy released if all the atoms in \(120 g\) of pure \({ }^{240} X\) undergo fission is \(........\times 10^{25}\,MeV\).\(\left(\right.\) Given \(\left.N_A=6 \times 10^{23}\right)\)

A perfectly dimagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field \(\overrightarrow{ B }\). Then the field inside the paramagnetic substance is:

In Young's double slits experiment, the position of \(5^{\text {th }}\) bright fringe from the central maximum is \(5\,cm\). The distance between slits and screen is \(1\,m\) and wavelength of used monochromatic light is \(600\,nm\). The separation between the slits is \(........\mu m\)

A wire of length \(L\, (=20\, cm)\), is bent into a semicircular arc. If the two equal halves of the arc were each to be uniformly charged with charges \( \pm Q\,,\,\left[ {\left| Q \right| = {{10}^3}{\varepsilon _0}} \right]\) Coulomb where \(\varepsilon _0\) is the permittivity (in \(SI\, units\)) of free space] the net electric field at the centre \(O\) of the semicircular arc would be

\(A\) and \(B\) are two sources generating sound waves. A listener is situated at \(C\) . The frequency of the source at \(A\) is \(500\,Hz\) . \(A,\) now, moves towards \(C\) with a speed \(4\,m/s.\) The number of beats heard at \(C\) is \(6.\) When \(A\) moves away from \(C\) with speed \(4\,m/s,\) the number of beats heard at \(C\) is \(18.\) The speed of sound is \(340\,m/s.\) The frequency of the source at \(B\) is ..... \(Hz\)

A car moving with a speed of \(54\) km/h takes a turn of radius \(20\) m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10\) m/s\(^2\))