an object tied to the end of a string moves in a circle. the force exerted by the string depends on the mass of the object, its speed, and the radius of the circle what combination of these variables gives the correct dimensions (ML/T2) for the force?

Question

an object tied to the end of a string moves in a circle. the force exerted by the string depends on the mass of the object, its speed, and the radius of the circle what combination of these variables gives the correct dimensions (ML/T2) for the force?

Answer 1

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Answer 2

To determine the combination of variables that gives the correct dimensions for force (ML/T²), we need to analyze the equation that relates force to the mass of the object, its speed, and the radius of the circle.

The equation for the force exerted by the string on the object moving in a circle is given by:

Force = (mass × speed²) / radius

Now, let's break down each term in this equation:

- mass (M): It represents the quantity of matter in the object and is denoted by the symbol "M".
- speed² (L²/T²): Speed is the rate at which an object covers a distance per unit time. When squared, it has dimensions of (L²/T²).
- radius (L): It represents the distance between the center of the circle and the object and is denoted by the symbol "L".

By substituting these terms into the equation and analyzing the dimensions, we get:

Force = (M × L²/T²) / L

Simplifying further:

Force = (ML²/T²) / L

Now, when we divide (ML²/T²) by L, we subtract the exponent of L in the numerator, which gives us:

Force = (ML²/T²) × L^-1

Simplifying this expression, we remove the negative exponent of L:

Force = ML²/T² × 1/L

Finally, rearranging the terms, we find the combination of variables that gives the correct dimensions for force (ML/T²):

Force = M × L²/T² × 1/L

= M × L² × L^-1 / T²

= M × L^(2-1) / T²

= M × L / T²

Hence, the correct combination of variables that gives the dimensions of force (ML/T²) is mass (M) multiplied by length (L) divided by time squared (T²).

an object tied to the end of a string moves in a circle. the force exerted by the string depends on the mass of the object, its speed, and the radius of the circle what combination of these variables gives the correct dimensions (ML/T2) for the force?

Physics

Indicate your specific subject in the "School Subject" box, so those with expertise in the area will respond to the question.

Physics

To determine the combination of variables that gives the correct dimensions for force (ML/T²), we need to analyze the equation that relates force to the mass of the object, its speed, and the radius of the circle.