Meghan and rachel each have bowling balls with the same mass. they both roll them as hard as they can and then measure the speed of each ball. meghan rolls her ball exactly half as fast as rachel. how do the forces the two girls applied to their balls differ? a) rachel used half the force that meghan did. b) rachel used twice the force that meghan did. c) meghan used twice the force that rachel did. d) without knowing the mass of the balls, we can not say.

consider the motion of bowling ball rolled by megan :

v₀ = initial velocity of the ball = 0 m/s

v = final velocity of the ball

a = acceleration of the ball

t = time of travel

using the kinematics equation

v = v₀ + a t

v = 0 + a t

a = v/t                                                            eq-1

consider the motion of bowling ball rolled by rachel :

v₀ = initial velocity of the ball = 0 m/s

v' = final velocity of the ball

a' = acceleration of the ball

t = time of travel

using the kinematics equation

v' = v'₀ + a' t

v' = 0 + a' t

a' = v' /t                                                    eq-2

dividing eq-1 by eq-2

a/a' = (v/t)/(v'/t)

a/a' = v /v'

Given that : v = v'/2

hence

a/a' = (v'/2) /v'

a/a' = 1/2

ma / ma' = 1/2

F/F' = 1/2

F = F'/2

hence Rachel used twice the force that Meghan did

so correct choice is B)

gas and liquid