A calorie is a unit of heat or energy and it equals about 4.2 J where `1J = 1 kg m^2s^(-2)c`. Suppose we employ a system of units in which the unit of mass equals a kg, the unit of length equals R m, the unit of time y s? Show that a calorie has a magnitude`4.2 a^(-1) beta(-2) gamma2` in terms of the new units.

1 kg m^2s^(-2) =…………g cm^2 s^(-2) .

Velocity of a particle depends upon t as V = A + Bt + Ct^2 . If velocity is in m/s, the unit of A will be :

Find a vector of magnitude 4 units in the direction fo the vector 2hati - hatj + 2hatk

If bara and barb are unit vectors and theta is the angle between them, show that frac(1)(2)[bara-barb] = sin frac(theta)(2)

f the radius of a circle increases at a constant rate 1/(2pi) unit per second, then find the rate of increase of its area, when the radius is 1 unit.

At what temperature r.m.s velocity of H_2 molecules is equal to that of oxygen molecule at 47^0 C?

The unit of length convenient on the nuclear scale is a fermi : 1 f = 10^(-15) m. Nuclear sizes obey roughly the following empirical relation : r = r_0A^(1/3) where r is the radius of the nucleus, A its mass number, and r_0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.