Answer to Question #148420 in Mechanics | Relativity for mwale

Question

two objects travelling around two different circular orbits with constant speed they both have the same acceleration but object a is travelling twice as object b.the orbit radius for object a is? and the orbit radius for object b

Answer 1

Solution

Relation between acceleration and velocity and radius

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

For object a

$a_a=\frac{v_a^2}{r_a}$

For object b

$a_b=\frac{v_b^2}{r_b}$

Given relation

$v_a=2v_b$

Therefore using given condition

$a_a=a_b$

$\frac{4v_b^2}{r_a}=\frac{v_b^2}{r_b}$

$r_a=4r_b$

This is relation between both radius.