Question

if the unit of force is 2N , length is 4m and velocity is 6m/s , what is the the unit of mass
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Answer 1

The unit of mass is 2/9 Kg.

Explanation:

Given that,

Force = 2N

Length = 4m

Velocity = 6m/s-1

We express mass in terms of force, length, and velocity;

m ∝ $F^{x} l^{y} v^{z}$

∵ m = K $F^{x} l^{y} v^{z}$

where K is a non-dimensional constant.

∵ [mass] = $[Force]^{x} [length]^{y} [velocity]^{z}$

∵ $[m^{1} l^{1} T^{0} ]$ = $[L^{1} T^{-2} ]^{x} [L^{1}]^{y} [L^{1} T^{-1} ] ^{z}$

∵ $[m^{1} l^{1} T^{0} ]$ = $m^x L^{x + y + z} T^{-2x - z}$

⇒ x = 1

x + y + z = 0

-2x - z = 0

by solving these equations, we get

x = 1, y = 1, & z = -1

For K = 1

[mass] = [Force]^1 [Length]^1 [Velocity]^-1

= [2N]^1 [4m]^1 [6m/s]^-1

= 2/9 Kg

Thus, the unit of mass is 2/9 Kg.

Learn more: unit of mass

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Answer 2

Answer:

2/9 ANSWER AND SOLUTION IS UP