If the units of force energy and velocity are 10n , 100j ,5m/s find the units of length , mass and time
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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.
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.
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