A ball weighing 100 g is attached to a string and swung around with a speed of 2 m/s. If the centripetal force exerted by the string is 0.5 N, what is the length of the string?

A) 0.08 m
B) 0.8 cm
C) 8 m
D) 80 cm

Assuming the ball is swung around in a circle parallel to the ground, it has a centripetal acceleration a of

a = v ² / R

where v is the tangential speed of the ball and R is the length of the string.

The tension in the string is 0.5 N, so by Newton's second law, the ball has acceleration

F = m a   →   a = F / m = (0.5 N) / (0.1 kg) = 5 m/s²

where m is the ball's mass.

Solve for R :

a = v ² / R   →   R = v ² / a = (2 m/s)² / (5 m/s²) = 0.8 m = 80 cm

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