# Raindrop Problem

QUESTION:

A spherical raindrop falling under constant gravity, grows by absorption of moisture from it's surroundings. The rate of increase of it's mass is proportional to the instantaneous surface area. Assuming that the raindrop starts with an infinitely small radius, determine its acceleration at time t.

SOLUTION:

where,

Therefore,

let us consider the ansatz,

So

Therefore,

# Optical Grating

QUESTION:

A diffraction grating used at normal incidence gives a line
in certain order superposed on another line   of the next higher order. If the angle of diffraction be ,  how many lines/cm, are there on the grating?

SOLUTION:

Given :

Also,  by the problem, the two lines get superposed in
and order.

QUESTION:

Many chemical reactions have an activation energy   which is about eV . Hence Show that rate of chemical reactions doubles when temperature is increased by from the room temperature.

SOLUTION:

At T=300K,  which is about room temperature, the probalility that a particular reaction occurs is proportional to .
If the temperature is increased to ,

The probability increases to

QUESTION:

Show that the error in truncating a convergent alternating infinite series after n terms is less than the ( n+1 ) th terms.

[Calcutta University Physics Model Solution]

SOLUTION:

# How to become a GOOD Theoretical Physicist

Nobel Prize wining Physicist  Gerard 't Hooft gave  an outstanding road map  how to become a good Theoretical Physicist.  Have a look at it...