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

Options

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

Answer

A

Explanation

`:' n_(1)u_(1)=n_(2)u_(2) :. N_(2)=(u_(1)/u_(2)) n_(1)=((M_(1)L_(1)T_(1)^(2))/(M_(2)L_(2)T_(2)^(-2)))(n_(1))`
`rArr n_(2)=[((1000g)(100 cm)(1)^(-2))/((10g)(10 cm)(0.1)^(-2))][1]=10`
`1N=10xx` Unit of force in new system
So unit of force in new system `=0.1 N`
OR
As `[F]=MLT^(-2)` so
unit of force `=(10g) (10 cm)(0.1 s)^(-2)`
`=(10^(-2) kg)(10^(-1) m)100(s)^(-2)`
`=0.1 (kg)(m)(s)^(-2)=0.1 N`