Answer :
To determine which equation correctly describes how to calculate the mass of an object given its acceleration and the net force acting on it, let's start with Newton's second law of motion.
According to Newton's second law of motion, the force [tex]\( F \)[/tex] acting on an object is the product of its mass [tex]\( m \)[/tex] and its acceleration [tex]\( a \)[/tex]. This relationship is mathematically represented as:
[tex]\[ F = m \cdot a \][/tex]
We need to find an equation that isolates the mass [tex]\( m \)[/tex]. To do this, we rearrange the equation to solve for [tex]\( m \)[/tex]. We divide both sides of the equation by the acceleration [tex]\( a \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
This equation tells us that the mass of an object is equal to the net force acting on it divided by its acceleration.
Now let's examine the given options:
A. [tex]\( m = F^{\circ} \)[/tex]
This option is not correct; [tex]\( F^{\circ} \)[/tex] does not relate to the equation [tex]\( F = m \cdot a \)[/tex].
B. [tex]\( m = \frac{a}{F} \)[/tex]
This option is incorrect because it suggests that the mass is the acceleration divided by the force, which contradicts [tex]\( m = \frac{F}{a} \)[/tex].
C. [tex]\( m = \frac{F}{a} \)[/tex]
This option is correct. It matches the equation we derived from Newton's second law, showing that the mass is the net force divided by the acceleration.
D. [tex]\( m = F \cdot a \)[/tex]
This option is incorrect because it suggests that the mass is the product of the force and the acceleration, which does not match Newton's second law.
Therefore, the correct equation showing how to calculate the mass of an object given its acceleration and the net force acting on it is:
[tex]\[ \boxed{m = \frac{F}{a}} \][/tex]
Thus, the correct answer is option C.
According to Newton's second law of motion, the force [tex]\( F \)[/tex] acting on an object is the product of its mass [tex]\( m \)[/tex] and its acceleration [tex]\( a \)[/tex]. This relationship is mathematically represented as:
[tex]\[ F = m \cdot a \][/tex]
We need to find an equation that isolates the mass [tex]\( m \)[/tex]. To do this, we rearrange the equation to solve for [tex]\( m \)[/tex]. We divide both sides of the equation by the acceleration [tex]\( a \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
This equation tells us that the mass of an object is equal to the net force acting on it divided by its acceleration.
Now let's examine the given options:
A. [tex]\( m = F^{\circ} \)[/tex]
This option is not correct; [tex]\( F^{\circ} \)[/tex] does not relate to the equation [tex]\( F = m \cdot a \)[/tex].
B. [tex]\( m = \frac{a}{F} \)[/tex]
This option is incorrect because it suggests that the mass is the acceleration divided by the force, which contradicts [tex]\( m = \frac{F}{a} \)[/tex].
C. [tex]\( m = \frac{F}{a} \)[/tex]
This option is correct. It matches the equation we derived from Newton's second law, showing that the mass is the net force divided by the acceleration.
D. [tex]\( m = F \cdot a \)[/tex]
This option is incorrect because it suggests that the mass is the product of the force and the acceleration, which does not match Newton's second law.
Therefore, the correct equation showing how to calculate the mass of an object given its acceleration and the net force acting on it is:
[tex]\[ \boxed{m = \frac{F}{a}} \][/tex]
Thus, the correct answer is option C.
