Question

If the units of force, energy and velocity in a new system are 10N, 5J and 0.5m/s respectively ,find the units of mass ,length and time in that system

Answer 1

$[Energy] = [Force]\times [length]$

Units of energy:

$1J= 1N\times m$

$[velocity] = \frac{[lenght]}{[time]}$

Units of velocity:

$m/s=\frac{m}{s}$

$[Force ] = [mass] \times[acceleration] = \frac{[mass]\times[velocity]}{[time]}= \frac{[mass]\times[length]}{[time]^2}$

Units of Force:

$1N = \frac{1kg\times m}{s^2}$

Obviously we can express length through force and energy

$[length] = \frac{[Energy]}{[Force]}$

Unit of length = unit of energy divide by unit of force

$\frac{5J}{10N}= \frac{5N\times m}{10N}=0.5m$

$[time] = \frac{[length]}{[velocity]}$

Unit of time= unit of velocity divide by unit of length

$\frac{0.5 m}{0.5\frac{m}{s}} = 1s$

$[mass] =\frac{[Force]\times[time]^2}{[length]}$

$\frac{10N\times s^2}{0.5m}=\frac{20{kg\times m}\times s^2}{m\times s^2}= 20 kg$

Units of length 0.5 meters

Units of time 1 second

Units of mass 20 kilograms