The decay rate of radium at any time `t` is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.

In a reaction the rate of reaction is proportional to its active mass, this statement is known as

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

If a point is moving in a line so that its velocity at time t is proportional to the square of the distance covered, then its acceleration at time t varies as

A particle which is four times in mass and two times in charge that of proton is called

A radioactive substance has a half-life of h days. Find a formula for its mass m in terms of time t if the initial mass is m_0 . What is its initial decay rate?

In the previous problem, if time period, T =2(pi) m/(BQ) where Q is the charge of the particle and m is its mass, the ratio of time spent by the particle in field when (theta) is positive to when (theta) is negative is given by

Fuel is consumed at the rate of 50 kg s^(-1) in a rocket. Find the thrust on the rocket if the velocity of the exhaust gases is 2 km s^(-1) . Also calculate the velocity of the rocket at the instant, when its mass is reduced to l/10th of its initial mass if its initial velocity is zero, (neglect gravity)

The half life of polonium is 140 days. In what time will 15 g of polonium be disintegrated out of its initial mass of 16 g ?

A radioactive sample contains two different types of radioactive nuclei. A-with half-time 5 days and B-type with half life 30 days. Initially the decay rate of A-type nuclei is 64 times that of B type of nuclei . Their decay rates will be equal when time is 9n days. Find the value of n.