Suchita makes a table to identify the variables used in the equations for centripetal force.

| Variable | Quantity |
|----------|--------------------|
| [tex]\(F_c\)[/tex] | |
| [tex]\(m\)[/tex] | |
| [tex]\(r\)[/tex] | [tex]\(X\)[/tex] |
| [tex]\(v\)[/tex] | [tex]\(Y\)[/tex] |

What quantities belong in cells [tex]\(X\)[/tex] and [tex]\(Y\)[/tex]?

A. [tex]\(X\)[/tex]: tangential speed, [tex]\(Y\)[/tex]: radius
B. [tex]\(X\)[/tex]: radius, [tex]\(Y\)[/tex]: tangential speed
C. [tex]\(X\)[/tex]: centripetal force, [tex]\(Y\)[/tex]: mass
D. [tex]\(X\)[/tex]: mass, [tex]\(Y\)[/tex]: centripetal force



Answer :

To identify the variables used in the equations for centripetal force and to fill in the cells [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] in the table provided by Suchita, we need to understand the meaning of the variables involved in the centripetal force equation. The standard equation for centripetal force ([tex]\(F_c\)[/tex]) is given by:

[tex]\[ F_c = \frac{m v^2}{r} \][/tex]

where:
- [tex]\(F_c\)[/tex] is the centripetal force,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(r\)[/tex] is the radius of the circular path,
- [tex]\(v\)[/tex] is the tangential speed.

From the context provided, the table indicates that the variable [tex]\(r\)[/tex] corresponds to the quantity [tex]\(X\)[/tex] and the variable [tex]\(v\)[/tex] corresponds to the quantity [tex]\(Y\)[/tex].

Therefore:
- [tex]\(X\)[/tex] should correspond to the radius,
- [tex]\(Y\)[/tex] should correspond to the tangential speed.

So, based on the identification of these variables in the equation for centripetal force, the correct quantities to fill in cells [tex]\(X\)[/tex] and [tex]\(Y\)[/tex] in the table are:

[tex]\[ X: \text{radius} \][/tex]
[tex]\[ Y: \text{tangential speed} \][/tex]