The ratio between the centripetal force of body in (A) to that in (B) is.?

Question

two bodies of the same mass in two different orbits (A) and (B) . if the radius of orbit (A) is double that of orbit (B) and the velocity of of the body in orbit (A) is double that of the body in orbit (B), the ratio between the centripetal force of body in (A) to that in (B) is....

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Answer 1 · 2018-04-03T00:26:13

#F_A : F_B = 2:1#

The centipretal force is given by

#F =( mv^2)/r#

Since #m_A = m_B#, #r_A = 2r_B# and #v_A = 2v_B#, we have

#F_A/F_B = m_A/m_B v_A^2/v_B^2 r_B/r_A = 1 times 2^2 times 1/2 = 2#