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# Check the correctness of the equation $F{\text{ }} = {\text{ }}\dfrac{{m{v^2}}}{r}$ where F is a force, m is mass, v is velocity and r is a radius.

Last updated date: 09th Aug 2024
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Hint: To solve this question, i.e., to check the correctness of the given equation. We will take standard formula of force, which is $F{\text{ }} = {\text{ }}m \times a.$ Then we will connect both the equations of force and the given equation, after converting those into their respective dimension formula, we will check whether both sides of the equation are equal or not, if it is equal, then the equation is correct, if not, then the equation will be incorrect.

We need to check the correctness of the equation given to us, which is, $F{\text{ }} = {\text{ }}\dfrac{{m{v^2}}}{r}$
where, F $=$ force, m $=$ mass, v $=$ velocity and r $=$ radius.
We know that, Force $=$ mass $\times$ acceleration, i.e., $F{\text{ }} = {\text{ }}m \times a........eq.(1)$
And the given equation of force is, $F{\text{ }} = \dfrac{{m{v^2}}}{r}........eq.(2)$
$\Rightarrow ma = \dfrac{{m{v^2}}}{r}$
$\Rightarrow {20}{l}{ML{T^{ - 2}} = M{L^2}{T^{ - 2}}{L^{ - 1}}} \\ \Rightarrow {ML{T^{ - 2}} = ML{T^{ - 2}}}$
Since, the dimension formula of Force and $\dfrac{{m{v^2}}}{r}$ are equal, therefore, the equation is dimensionally correct.