A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of \(5\) times its mass? (Assume the collision to be head-on elastic collision)

When the wavelength of radiation falling on a metal is changed from \(500 \,nm\) to \(200\, nm ,\) the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to\(.....eV\)

The co-ordinates of a particle moving in \(x-y\) plane are given by :  \(\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .\) The motion of the particle is _______.

In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ]

A light wave described by \(E =60 \sin \left(3 \times 10^{15}\right) t + \sin \left(12 \times 10^{15}\right)\) t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately) _________ eV .

In the figure shown \(ABC\) is a uniform wire . If centre of mass of wire lies vertically below point \(A\) , then \(\frac{{BC}}{{AB}}\) is close to 

The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

If \(C\) and \(V\) represent capacity and voltage respectively then what are the dimensions of \(\lambda,\) where \(\frac{ C }{ V }=\lambda ?\)

The total current supplied to the circuit as shown in figure by the \(5 V\) battery is \(A\)

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be

A massless spring \((k = 800\, N/m)\), attached with a mass \((500\, g)\) is completely immersed in \(1\, kg\) of water. The spring is stretched by \(2\, cm\) and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass \(= 400\, J/kg\, K\), specific heat of water \(= 4184\, J/kg\, K\))