Two planets \(A\) and \(B\) having masses \(m_1\) and \(m_2\) move around the sun in circular orbits of \(r_1\) and \(r_2\) radii respectively. If angular momentum of \(\mathrm{A}\) is \(\mathrm{L}\) and that of \(B\) is \(3L\), the ratio of time period \(\left(\frac{T_A}{T_B}\right)\) is _______.

A radioactive sample decays \(\frac{7}{8}\) times its original quantity in \(15\) minutes. The half-life of the sample is \(......min\)

Muon \((\mu ^{-1})\) is negatively charged \(\left( {\left| q \right| = \left| e \right|} \right)\) with a mass \(m_{\mu}\, = 200\,m_e\), where \(m_e\) is the mass of the electron and \(e\) is the electronic charge. If \(\mu ^{-1}\) is bound to a proton to form a hydrogen like atom, identify the correct statements \((A)\) Radius of the muonic orbit is \(200\) times smaller than that of the electron \((B)\) the speed of the \(\mu ^{-1}\) in the \(n^{th}\) orbit is \(\frac{1}{{200}}\) times that of the election in the \(n^{th}\) orbit \((C)\) The Ionization energy of muonic atom is \(200\) times more than that of an hydrogen atom \((D)\) The momentum of the muon in the \(n^{th}\) orbit is \(200\) times more than that of the electron

The ratio of intensities at two points \(P\) and \(Q\) on the screen in a Young's double slit experiment where phase difference between two wave of same amplitude are \(\pi / 3\) and \(\pi / 2\), respectively are

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 :

A cylindrical wire of mass \((0.4 \pm 0.01)\,g\) has length \((8 \pm 0.04)\,cm\) and radius \((6 \pm 0.03)\,mm\).The maximum error in its density will be \(......\,\%\)

A particle initially at rest starts moving from reference point. \(\mathrm{x}=0\) along \(\mathrm{x}\)-axis, with velocity \(v\) that varies as \(v=4 \sqrt{\mathrm{x} m} / \mathrm{s}\). The acceleration of the particle is _______ \( \mathrm{ms}^{-2}\).

Match List \(- I\) (Fundamental Experiment) with List \(- II\) (its conclusion) and select the correct option from the choices given below the list \(\begin{array}{|||} \hline List\,\,-1  & List\,\,-II\,\,  \\ \hline a\,\,Franck-Hertz\,\,Experiment & i\,\,Particle\,\,nature\,\,of\,\,light \\ \hline b\,\,Photo\,\,-electric\,\,Experiment & ii\,\,Discrete\,\,energy \,\, levels\,\,of\,\,atom \\ \hline c\,\,Davison-Germer\,\,Experiment & iii\,\,Wave\,\,nature\,\,of\,\,electron \\ \hline  & iv\,\,Structure\,\,of\,\,atom  \\ \hline \end{array}\)

A bob of mass ' \(m\) ' is suspended by a light string of length ' \(L\) '. It is imparted a minimum horizontal velocity at the lowest point \(A\) such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \(\frac{(\text { K.E. })_A}{(\text { K.E. })_B}\) is _______.