A 0.25kg ball moving in a horizontal cirlce at the end of a string has a...

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A 0.25kg ball moving in a horizontal cirlce at the end of astring has a centripetal acceleration of 4m/s^2. What is themagnitude of the centripetal force exerted by the string on theball to produce this acceleration?

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Magnitude of the centripetal force exerted by the string on the ball to produce this acceleration which is given as :

centripetal force given by, F_c = m v² / rÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â { eq.1 }

centripetal force given by, a_c = v² / rÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â { eq.2 }

equating above two eq. we get

F_c = m a_cÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â { eq.3 }

where, m = mass of the ball = 0.25 kg

a_c = centripetal acceleration = 4 m/s²

inserting the values in eq.3,

F_c = (0.25 kg) (4 m/s²)

F_c = 1 N

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