Question

The force experienced by a mass moving with a uniform speed v in a circular path of radius r experiences a force which depends on it's mass, speed and radius prove that the relation is f=mv2.

Answer 1

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Answer 2

Step-by-step explanation:

It is given that the force experienced by a mass moving with a uniform speed v in a circular path of radius r experiences a force which depends on its mass, speed and radius.

Step 1:

$f ∝ {m}^{a} {v}^{b} {r}^{c}$

$f ∝ [{m}]^{a} [{v}]^{b} [{r}]^{c}$

Step 2: But,

$f = {M} L{T}^{- 2}$

and

$m = {M} ^{a}$

$v = { LT}^{- 1}$

$r = { L}^{c}$

So,

${M} L{T}^{- 2} \: = {[ {M}]^{a} [ L{T}^{- 1}}]^{b} [ {L}^{c} ]$

Step 3: Compare the powers of both sides,

for M: a = 1

for L: 1 = b + c

for T: -2 = -b

so, b = 2

Putting b =2 in 1 = b+c

So, 1 = 2 + c

c = -1

Step 4: By putting the above a,b and c value in the below equation,

${M} L{T}^{- 2} \: = {[ {M}]^{a} [ L{T}^{- 1}}]^{b} [ {L}^{c} ]$

So, $f = \frac{m {v}^{2} }{r}$is correct.

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