Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \(5^{\text {th}}\) orbit of the electron in \(\mathrm{Li}^{2+}\) and \(\mathrm{He}^{+}\) is _______.

If time \((t)\), velocity \((u)\), and angular momentum \((I)\) are taken as the fundamental units. Then the dimension of mass \(({m})\) in terms of \({t}, {u}\) and \({I}\) is

The magnetic field of an electromagnetic wave is given by \(\vec B = 1.6 \times {10^{ - 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}\) The associated electric field will be

A simple harmonic oscillator has an amplitude \(A\) and time period \(6 \pi\) second. Assuming the oscillation starts from its mean position, the time required by it to travel from \(x=A\) to \(x=\frac{\sqrt{3}}{2} A\) will be \(\frac{\pi}{x}\) s, where \(x=\) _______.

A pressure-pump has a horizontal tube of cross-sectional area \(10\,cm ^{2}\) for the outflow of water at a speed of \(20\,m / s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is \(...N\) [given : density of water \(=1000\,kg / m ^{3}\) ]

Two short magnetic dipoles \({m}_{1}\) and \({m}_{2}\) each having magnetic moment of \(1\, {Am}^{2}\) are placed at point \({O}\) and \(P\) respectively. The distance between \(OP\) is \(1\, meter.\) The torque experienced by the magnetic dipole \({m}_{2}\) due to the presence of \({m}_{1}\) is ...... \(\times 10^{-7}\, {Nm}\)

The equivalent capacitance between \(A\) and \(B\) in the circuit given below is.....\(μF\)

A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density \(+\sigma\) and \(-2 \sigma\). The force experienced by a point charge +q placed at the mid point between two plates will be :

If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )