In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to

Options

A. 0.1 N
B. 1N
C. 10N
D. 100N

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)= 1[(10kg)/(1kg)]^(1)[(10cm)/(1m)^(1)][(0.1s)/(1s)]^(-2)`
`= 1((10^(-2)kg)/(1kg))^(1)((10^(-1)m)/(1m))^(1)((0.1s)/(1s))^(-2)`
`= ( 1xx 10^(-2) xx10^(-1))/(10^(-2))= 10^(-1)= 0.1 `
hence, the unit of force in a given system will be equivalent to 0.1 N.