Question

If the unit of force energy and velocity are 10 newton 100 joules and 10 m per second find the unit of length mass and time

Answer 1

The Dimensional formulae of 
force = [ MLT^-2 ]
energy = [ML²T^-2]
velocity = [LT^-1]
Thus We have 
[MLT^-2] = 10N.......(i)
[ML²T^-2] = 100J .....(ii)
[LT-1] = 5ms^-1 .......(iii) 
and
Dividing equation (ii) by eq.(i) ,we have 
[L] = 100J/10N = 100Nm/10N = 10m.
Substituting the unit of [L] in eq. (iii) , we have
[T^-1] = 5ms^-1/[L] = 5ms^-1/ 10m
[ T ] = 10m/5ms^-1 = 2s.
Substituting the units of [L] and [ T] in eq.( i) we have
[M] = 10N / [L] [T^-2] = 10N × 4s² / 10m = 4kg.