When one metre, one kg and one minute are taken as fundamental units, the magnitude of a force is 36 units. What is the value of this force on CGS system?

Options

A. `10^(3)` dyne
B. `10^(5)` dyne
C. `10^(6)` dyne
D. `10^(7)` dyne

Answer

A

Explanation

The dimensional formula of force is `[MLT^(-2)]`
`:. a= 1, b= 1, c=-2`
`n_(2)= n_(1)[(M_(1))/(M_(2))]^(a)[(L_(1))/(L_(2))]^(b)[(T_(1))/(T_(2))]^(c)= 36[(1kg)/(1g)]^(1)[(am)/(1cm)^(1)][(1min)/(1s)]^(-2)`
`= 36[(1000g)/(1g)]^(1)[(100cm)/(1cm)^(1)][(60s)/(1s)]^(-2)= (36 xx10^(3) xx 10^(2))/(3600)= 10^(3)`
Hence, in the CGS system of units the value of given force is `10^(3)` dyne