Question

if the unit of length ,mass and time are doubled the unit of force will be changed or unchanged

Answer 1

Given the fundamental units of length,velocity and force are doubled.
⇒Length Dimensions are =L

⇒V=Displacement /Time
Velocity Dimensions= LT⁻¹
In order to make velocity  double , already length is doubled.
So no change in Time.

⇒Force=ma
Force dimensions=MLT⁻²
already length is doubled to make force double .
So no change will be there in mass . It will be constant

Answer 2

Answer:

If the fundamental units of force are doubled, the unit of force remains unchanged.

Explanation:

Given the fundamental units length, mass and time are doubled.

Dimension of Length is $[L]$

Dimension of mass is $[M]$

And dimension of time is $[T]$

Force is defined as mass times acceleration, and is given by

$F=m\times a=m\times \frac{v}{t}$

Writing the dimensions for force,

$[F]=\frac{[M^{1} ][L^{1} ]}{[T^{2} ]}$

If the units are doubled,

$[F]==\frac{[2M^{1} ][2L^{1} ]}{[(2T)^{2} ]}$

$=\frac{[2M^{1} ][2L^{1} ]}{[4T^{2} ]}$

$=\frac{[M^{1} ][L^{1} ]}{[T^{2} ]}$

$=[M^{1} L^{1} T^{-2} ]$

Therefore, there is no change in the unit of force.

Therefore, if the fundamental units of force are doubled, the unit of force remains unchanged.