The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point , \(P\), located as shown, would be (nearly)

Radiation coming from transition \(n = 2\) to \(n = 1\) of hydrogen atoms fall of \(He^+\) ions in \(n = 1\) and \(n = 2\) states. The possible. Transition of helium ions as they absorb energy from the radiation is

A source of sound \(A\) emitting waves of frequency \(1800\,Hz\) is falling towards ground with a terminal speed \(v.\) The observer \(B\) on the ground directly beneath the source receives waves of frequency \(2150\,Hz.\) The source \(A\) receives waves, reflected from ground of frequency nearly ..... \(Hz\) (Speed of sound \(= 343\,m/s\) )

\(2\, kg\) of a monoatomic gas is at a pressure of \(4\times10^4\, N/m^2\). The density of the gas is \(8\, kg/m^3\). What is the order of energy of the gas due to its thermal motion ?

A student measured the length of a rod and wrote it as \(3.50\;cm\). Which instrument did he use to measure it?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A:\) Alloys such as constantan and manganin are used in making standard resistance coils. Reason \(R:\) Constantan and manganin have very small value of temperature coefficient of resistance.In the light of the above statements, choose the correct answer from the options given below.

A cylindrical conductor of length 2m and area of cross-section \( 0.2\,mm^{2} \) carries an electric current of 1.6 A when its ends are connected to a 2V battery. Mobility of electrons in the conductor is \( \alpha\times10^{-3} m^{2}/V.s \). The value of \( \alpha \) is:
(electron concentration \( =5\times10^{28}/m^{3} \) and electron charge \( =1.6\times10^{-19} C \))

Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}=B_0\sin\left(2\pi vt-\dfrac{2\pi x}{\lambda}\right)\hat{j}\). Its associated electric field vector is ______.

A glass tumbler having inner depth of \(17.5\, {cm}\) is kept on a table. A student starts pouring water \((\mu=4 / 3)\) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ? (In \(cm\))

Consider two ideal diatomic gases \(\mathrm{A}\) and \(\mathrm{B}\) at some temperature \(T\). Molecules of the gas \(A\) are rigid, and have a mass \(m\). Molecules of the gas \(\mathrm{B}\) have an additional vibrational mode, and have a mass \(\frac{\mathrm{m}}{4} .\) The ratio of the specific heats \((\mathrm{C}_{\mathrm{v}}^{\mathrm{A}}\) and \(\mathrm{C}_{\mathrm{v}}^{\mathrm{B}})\) of gas \(\mathrm{A}\) and \(\mathrm{B}\), respectively is