A radioactive source, in the form of a metallic sphere of radius `10^(-2)m` emits `beta`-particles at the rate of `5xx10^(10)` particles per second. The source is electrically insulated. How long will it take for its potential to be raised by 2V, assuming that 40% of the emitted` beta`-particles escape the source.

Water flows a the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface is 40 cm and depth 24cm^2 .

The atomic weiht of radium is 226 .It is observed that 3.67 xx 10^(10) alpha - particles are emitted per second from one gramp of radium.Calculate in years the half-life period of radium.

A certain particle carries 2. 5 xx 10 ^(-16) C of static electric charge. Calculate the number of electrons present in it.

Assertion: A metal sphere of radius 1 cm can not hold a charge of 1 coulomb Reason: For placing a charge of 1 coulomb on a shere of radius 1 cm, its potential has to eb raised to = 9 xx 10^22 V

In a photoelectric effect set up, a point source of light of power 3.2 xx10^(-3) W emits monoenergetic photons of energy 5eV.The source is located at a distance of a stationary metallic sphere of work function 3eV and radius 8xx10^(-3)m .The efficiency of photoelectron emission is one for every 10^(6) incident photons.Assume that the sphere is isolated and initially neutral and the photoelectrons are initially swept away after emission. Calculate the number of photoelectrons emitted per second.

A fresh radioactive mixture contians short lived sppecies A and B. Both emitting alpha -particles intially of 8000 alpha particles per minute. 20 minutes later, they emis at the rate of 3500 alpha -particles per minute. If the half-lives of the species A and B are 10 minutes and 500 hours respectively, then the ratio of activities of A: B the intial mixture was:

A coil has an inductance of 1.5 xx 10^-2 H. Calculate the e.m.f. induced, when current in the coil changes at the rate 200 ampere per second.

In a photoelectric effect set up, a point source of light of power 3.2 xx10^(-3) W emits monoenergetic photons of energy 5eV.The source is located at a distance of a stationary metallic sphere of work function 3eV and radius 8xx10^(-3)m .The efficiency of photoelectron emission is one for every 10^(6) incident photons.Assume that the sphere is isolated and initially neutral and the photoelectrons are initially swept away after emission. Find the ratio of the wavelength of incident light to the de Broglie wavelength of the fastest phtotelectrons emitted.