Question

An object traveling a circular path of radius 5 m at constant speed experiences an acceleration of 3 m/s2. If the radius of its path is increased to 10 m, but its speed remains the same, what is its acceleration?

Answer 1

Answer:

New acceleration = 1.5 m/s²

Explanation:

The acceleration of an object when it moves in a circular path is given by :

$a=\dfrac{v^2}{r}$

Where

v is speed of an object

r is radius of path

If v remains constant,

$a\propto \dfrac{1}{r}$

or

$\dfrac{a_1}{a_2}=\dfrac{r_2}{r_1}$

Put r₁ = 5 m, a₁ = 3m/s², r₂ = 10 m

$a_2=\dfrac{a_1r_1}{r_2}\\\\a_2=\dfrac{3\times 5}{10}\\\\a_2=1.5\ m/s^2$

Hence, if the radius of its path is increased to 10 m, its acceleration will be 1.5 m/s².