Question

How do you solve for $ v $ in $ Fc = \dfrac{{m{v^2}}}{r} $ ?

Answer 1

Hint: There is no calculation or solving part in this question. Just move the constants form right to left except $ v $ . First multiply $ r $ on both the sides, then divide both sides by $ m $ . Then Square roots both the sides so that we obtain our constant $ v $ and their value from this formula.

Complete step by step solution:
The Equation given is $ Fc = \dfrac{{m{v^2}}}{r} $ .
We have to solve for $ v $ from the given equation. Basically, we have to separate $ v $ on the right side by multiplying or dividing the constants.
So, let's start with the first step:
Multiplying both sides with $ r $ to cut out $ r $ or move $ r $ from the right to left side and we get:
 $
  Fc.r = \dfrac{{m{v^2}}}{r} \times r \\
  Fc.r = m{v^2} \;
  $
Now, we are left with $ m $ and $ v $ , we have to remove $ m $ so that we are left with our needed value or result that is only $ v $ .
For the second step, divide both the sides by $ m $ to get only $ v $ alone on the right side and no other constants with it and we get:
\[
 \Rightarrow Fc.r = \dfrac{{m{v^2}}}{r} \times r \\
 \Rightarrow Fc.r = m{v^2} \\
 \Rightarrow \dfrac{{Fc.r}}{m} = \dfrac{{m{v^2}}}{m} \\
 \Rightarrow \dfrac{{Fc.r}}{m} = {v^2} \;
 \]
For the next and the last step that is square root both the sides (because there is $ {v^2} $ and we want the value of $ v $ )and we get:
\[
 \Rightarrow Fc.r = \dfrac{{m{v^2}}}{r} \times r \\
 \Rightarrow Fc.r = m{v^2} \\
 \Rightarrow \dfrac{{Fc.r}}{m} = \dfrac{{m{v^2}}}{m} \\
  \dfrac{{Fc.r}}{m} = {v^2} \\
 \Rightarrow \sqrt {\dfrac{{Fc.r}}{m}} = \sqrt {{v^2}} \\
 \Rightarrow \sqrt {\dfrac{{Fc.r}}{m}} = v \;
 \]
Therefore, the value of $ v $ in $ Fc = \dfrac{{m{v^2}}}{r} $ is \[v = \sqrt {\dfrac{{Fcr}}{m}} \].


So, the correct answer is “\[v = \sqrt {\dfrac{{Fcr}}{m}} \]”.

Note: There is nothing in this question just moving of constants to get the value of $ v $ so, don’t try to put up the formulas or values which would complicate the steps.
Don’t leave $ {v^2} $ as it is because we want the value of $ v $ and not of $ {v^2} $ , which could change the answer.