A man of \(60\,kg\) is running on the road and suddenly jumps into a stationary trolly car of mass \(120\,kg\). Then. the trolly car starts moving with velocity \(2\,ms ^{-1}\). The velocity of the running man was _________\(ms ^{-1}\). when he jumps into the car

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). \(Assertion\) \(A\) : Number of photons increases with increase in frequency of light. \(Reason\) \(R\) : Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation. In the light of the above statements, choose the most appropriate answer from the options given below :

In a resonance tube experiment when the tube is filled with water up to height of \(17.0\, cm\) from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of \(24.5\, cm\). If the velocity of sound in air is \(330\, m / s ,\) the tuning fork frequency is\(......Hz\)

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed \(\left(v_{ ms }\right)\) and choose the correct answer from the options given below:

A string of length \(L\) is fixed at one end and carries a mass of \(M\) at the other end. The mass makes \(\left(\frac{3}{\pi}\right)\) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is \(\ldots\ldots\) ML.

A circuit element \(X\) when connected to an a.c. supply of peak voltage \(100\,V\) gives a peak current of \(5\,A\) which is in phase with the voltage. A second element \(Y\) when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by \(\frac{\pi}{2}\). If \(X\) and \(Y\) are connected in series to the same supply, what will be the rms value of the current in ampere?

In the equation \(\left[X+\frac{a}{Y^2}\right][Y-b]= R T, X\) is pressure, \(Y\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is

A cylindrical container of volume \(4.0 \times 10^{-3} \,{m}^{3}\) contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is \(400 \,{K}\) The pressure of the mixture of gases is: [Take gas constant as \(8.3\, {J} {mol}^{-1} {K}^{-1}\)]