in the equation for centripetal force, which expression represents the centripetal acceleration of the…

in the equation for centripetal force, which expression represents the centripetal acceleration of the object?\n$mv^{2}$\n$\frac{m}{r}$\n$\frac{v^{2}}{r}$\n$\frac{mv^{2}}{r}$

in the equation for centripetal force, which expression represents the centripetal acceleration of the object?\n$mv^{2}$\n$\frac{m}{r}$\n$\frac{v^{2}}{r}$\n$\frac{mv^{2}}{r}$

Answer

Explanation:

Step1: Recall centripetal - force formula

The centripetal - force formula is $F_c = ma_c$, where $F_c$ is the centripetal force, $m$ is the mass of the object, and $a_c$ is the centripetal acceleration. Also, the centripetal - force formula in terms of velocity is $F_c=\frac{mv^{2}}{r}$.

Step2: Solve for centripetal acceleration

Since $F_c = ma_c$ and $F_c=\frac{mv^{2}}{r}$, we can set $ma_c=\frac{mv^{2}}{r}$. Divide both sides of the equation by $m$ (assuming $m\neq0$). We get $a_c=\frac{v^{2}}{r}$.

Answer:

$\frac{v^{2}}{r}$