Which of the following equations represents a travelling wave ?

A proton and an \(\alpha\) -particle, having kinetic energies \(K _{ p }\) and \(K _{\alpha},\) respectively, enter into \(a\) magnetic field at right angles. The ratio of the radii of trajectory of proton to that of \(\alpha\) -particle is \(2: 1 .\) The ratio of \(K _{ p }: K _{\alpha}\) is :

A uniform solid cylindrical roller of mass \('m'\) is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is \('a'\) and it is rolling without slipping then the value of \('F'\) is 

A planet \((P_1)\) is moving around the star of mass \(2M\) in the orbit of radius \(R\). Another planet \((P_2)\) is moving around another star of mass \(4M\) in a orbit of radius \(2R\). Ratio of time periods of revolution of \(P_2\) and \(P_1\) is _______.

A boy ties a stone of mass \(100 \,g\) to the end of a \(2\) \(m\) long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of \(80 \,N\). If the maximum speed with which the stone can revolve is \(\frac{ K }{\pi} rev\). / \(min\). The value of \(K\) is (Assume the string is massless and unstretchable)

A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))

In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\  \Omega\). The power consumption in the entire circuit is _______ \(W\).

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

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

In an adiabatic process, which of the following statements is true?

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

A wire of length \(L\) is hanging from a fixed support. The length changes to \(L _{1}\) and \(L _{2}\) when masses \(1 \,kg\) and \(2 \,kg\) are suspended respectively from its free end. Then the value of \(L\) is equal to ..................

A uniform rod \(A B\) of mass \(2 \mathrm{~kg}\) and Length \(30 \mathrm{~cm}\) at rest on a smooth horizontal surface. An impulse of force \(0.2\  \mathrm{Ns}\) is applied to end \(B.\) The time taken by the rod to turn through at right angles will be \(\frac{\pi}{\mathrm{x}}\ \mathrm{s}\), where  X = _______.

Consider two containers \(A\) and \(B\) containing monoatomic gases at the same Pressure \((P)\), Volume \((V)\) and Temperature \((T)\). The gas in \(A\) is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas \(B\) is compressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in \(B\) to that of gas in \(A\) is ...........