Convert a work of 100 J into a system of units which has unit of mass as 100g, unit of length as 10cm and unit of time as 30s.
Ans: \(\)
A quantity of \(3600J.h^{-1}\) is converted into a system which measures the units of mass, length and time as 100g, 100cm and 1 min. respectively. Find: the value in new unit?
Ans: \(\left(9\times10^{7}\right)\) in new unit system.
If the unit of force is considered as \(200N\), that of power is \(10^{8}W\) and that of time is \(1ms\), then find unit of length?
Ans: \(500m\) in new unit system.
A calorie is the unit of heat or energy and it equals about \(4.2J\) where; \(1J=1Kg.m^{2}.s^{-2}\). Suppose we employ a new system of units in which the unit of mass is equal to \(\alpha Kg\), unit of length equals to \(\beta m\) and unit of time equals to \(\gamma s\). Show that the calorie has magnitude \(4.2\alpha^{-1}\beta^{-2}\gamma^{2}\) in terms of new units.
Ans: \(1Cal=4.2\alpha^{-1}\beta^{-2}\gamma^{2}\).
The unit of force is \(1kN\), unit of length \(1 km\) and unit of time is \(100 s\), what will be unit of mass?
Ans: \(M=10^{4}Kg\).
Power of an electric bulb is \(500W\). Express it in C.G.S system?
Ans: \(\left(5\times10^{9}\right)erg.s^{-1}\).
If, the unit of force, energy and velocity are \(20N\), \(200J\) and \(5ms^{-1}\). Find: the unit of length, mass and time?
Ans: \(10m,8Kg,2s\)
Convert \(5J\) into erg using dimensional analysis.
