Q39 of 44 Page 9

In the expression P = E l2 m-5 G-2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.

Given:


Equation of P = E l2 m-5 G-2


The dimensional equation of energy E is [M2L1T-2], for mass m is [M1L0T0], for length l is [M0L1T0] and for gravitational constant G is [M-1L3T-2].


Now to prove that P is a dimensionless quantity we have to find, the dimensional formula for P. For this, we substitute the dimensional formulae of the above quantities in the expression for P




Hence, P is a dimensionless quantity.


More from this chapter

All 44 →
37

The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as


where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML-1 T-1. Check whether the equation is dimensionally correct.


 38

A physical quantity X is related to four measurable quantities a, b, c and d as follows:

X = a2 B3 c5/2 d-2


The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X ? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.


 40

If velocity of light c, Planck’s constant h and gravitational constant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.

 41

An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that

T =


where k is a dimensionless constant and g is acceleration due to gravity.