A \(60\; HP\) electric motor lifts an elevator having a maximum total load capacity of \(2000\; \mathrm{kg}\). If the frictional force on the elevator is \(4000 \;\mathrm{N}\). the speed of the elevator at full load is close to ..............  \(\mathrm{m} / \mathrm{s}\) \(\left(1 \;\mathrm{HP}=746 \;\mathrm{W}, \mathrm{g}=10\; \mathrm{ms}^{-2}\right)\)

A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are \({\lambda _1}\) and \({\lambda _2}\), their de Broglie wavelength in the frame of reference attached to their centre of mass is

For the four sets of three measured physical quantities as given below. Which of the following options is correct ? \((i)\) \(\mathrm{A}_{1}=24.36, \mathrm{B}_{1}=0.0724, \mathrm{C}_{1}=256.2\) \((ii)\) \(\mathrm{A}_{2}=24.44, \mathrm{B}_{2}=16.082, \mathrm{C}_{2}=240.2\) \((iii)\) \(\mathrm{A}_{3}=25.2, \mathrm{B}_{3}=19.2812, \mathrm{C}_{3}=236.183\) \((iv)\) \(\mathrm{A}_{4}=25, \mathrm{B}_{4}=236.191, \mathrm{C}_{4}=19.5\)

Consider the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), where \(H=\) magnetic field; \(E=\) electric field, \(\epsilon=\) permittivity, \(x=\) distance, \(t=\) time. The values of \(p, q, r\) and \(s\) respectively are:

A conical pendulum of length \(1\,m\) makes an angle \(\theta \, = 45^o\) w.r.t. \(Z-\) axis and moves in a circle in the \(XY\) plane.The radius of the circle is \(0.4\, m\) and its centre is vertically below \(O\). The speed of the pendulum, in its circular path, will be ..... \(m/s\) (Take \(g\, = 10\, ms^{-2}\))

A series \(LR\) circuit is connected to an ac source of frequency \(\omega \) and the inductive reactance is equal to \(2R\). A capacitance of capacitive reactance equal to \(R\) is added in series with \(L\) and \(R\). The ratio of the new power factor to the old one is

In the given circuit, the charge on \(4\, \mu F\) capacitor will be.....\(\mu C\)

The correct match between the entries in column \(I\) and column \(II\) are              \(I\)                         \((II)\) Radiation                     Wavelength \((a)\) Microwave          \((i)\) \(100 m\) \((b)\) Gamma rays      \((ii)\) \(10^{-15} m\) \((c)\) \(A.M.\) radio waves        \((iii)\) \(10^{-10} m\) \((d)\) \(X-\)rays             \((iv)\) \(10^{-3} m\)

A man in a car at location \(Q\) on a straight highway is moving with speed \(v\). He decides to reach a point \(P\) in a field at a distance \(d\) from highway (point \(M\) ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance \(RM\), so that the time taken to reach \(P\) is minimum?

A particle of mass \(2\, kg\) is on a smooth horizontal table and moves in a circular path of radius \(0.6\, m\). The height of the table from the ground is \(0.8\, m\). If the angular speed of the particle is \(12\, rad\, s^{-1}\), the magnitude of its angular momentum about a point on the ground right under the centre of the circle is ........ \(kg\, m^2\,s^{-1}\)

Choose the incorrect statement : \((a)\) The electric lines of force entering into a Gaussian surface provide negative flux. \((b)\) A charge ' \(q\) ' is placed at the centre of a cube. The flux through all the faces will be the same. \((c)\) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. \((d)\) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given below