Question

the factors affecting force are mass and its acceleration, deduce the correct relationship using the method of dimension​

Answer 1

F=ma

Derivation:

It's a vector quantity.

Momentum is mv.

Let's consider a object with initial and final velocity, therefore,

P=mu(initial velocity)

P=mv(final velocity)

Let's subtract final from initial,

mv-mu

Let the rate of change of momentum be,

(mv-mu)/t =>m(v-u)/t

a=(v-u)/t

Therefore,

F=m(a)

Therefore we got F=ma

Answer 2

Explanation:

According to question,

Force is directly proportional to the mass and acceleration.

F ∝ $m^{a} a^{b}$

F = k $m^{a} a^{b}$        (where k is constant)

[$MLT^{-2}$] = $[M]^{a}$ $[LT^{-2} ]^{b}$

[$MLT^{-2}$] = $[M]^{a}$ $[L]^{b}$$[T]^{-2b}$

After comparing,

a = 1

b = 1

F = k $m^{a} a^{b}$        (where k is constant)

F = k m a

F = m a             (k = 1, Experimentally)

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