The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth.

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation \(d\) in terms of wavelength \(\lambda \) such that the first minima occurs directly in front of the slit \((S_1)\)?

The dimensional formula of \(\dfrac{1}{2}\epsilon_0 E^2\) (\(\epsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^a L^b T^c\). The value of \(2a - b + c = \) _______.

The box of a pin hole camera, of length \(L\), has a hole of radius \(a\). It is assumed that when the hole is illuminated by a parallel beam of light of wavelength \(\lambda\), the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size ( say \(b_{min}\)) when

The graph shows variation of stopping potential \(V_o\) with the frequency \(\nu\) of the incident radiation for three photosensitive metals \(X_1\), \(X_2\) and \(X_3\). Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm . Total magnification obtained with this system for normal adjustment is \((5)^{ k }\). The value of k is _________

In the arrangement shown in figure \(a _{1}, a _{2}, a _{3}\) and \(a _{4}\) are the accelerations of masses \(m _{1}, m _{2}, m _{3}\) and \(m _{4}\) respectively. Which of the following relation is true for this arrangement?

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is 

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

Light is incident normally on a completely absorbing surface with an energy flux of \(25\,W\,cm^{-2}.\) If the surface has an area of \(25\,cm^2,\) the maximum momentum transferred to the surface in \(40\,min\) time duration will be

The kinetic energy of translation of the molecules in 50 g of \(\mathrm{CO}_2\) gas at \(17^{\circ} \mathrm{C}\) is