A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains ? (Take ln 3 = 1.1)

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0.2 m/s². The normal reaction R' by the floor if mass of the iron cylinders are equal and of 20 kg each, is ____________ N. [Take g = 10 m/s² and $$\mu$$_s = 0.2]

A nucleus of mass M emits $$\gamma$$ -ray photon of frequency 'v'. The loss of internal energy by the nucleus is :

[Take 'c' as the speed of electromagnetic wave]

The radiation corresponding to 3 $$\to$$ 2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of 5 $$\times$$ 10^$$-$$4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is : (Mass of electron = 9.1 $$\times$$ 10^$$-$$31 kg)