A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution?
A) 4.8 s
B) 3.8 s
C) 4.5 s
D) 5.2 s

Question

Quizplus · Accepted Answer

The correct answer is A.Explanation:The tension in the string provides the centripetal force necessary to keep the mass moving in a circle. The centripetal force is given by:$$F_c = mv^2/r$$where:* Fc is the centripetal force* m is the mass* v is the speed* r is the radius of the circleThe tension in the string is equal to the centripetal force, so:$$T = mv^2/r$$We can solve this equation for v:$$v = sqrt(Tr/m)$$The period of revolution is the time it takes for the mass to make one complete revolution. The period is given by:$$T = 2πr/v$$We can substitute the expression for v into this equation:$$T = 2πr sqrt(m/T)$$We can solve this equation for T:$$T = 2π sqrt(mr/T)$$We can plug in the given values:$$T = 2π sqrt(23 kg * 1.3 m / 51 N)$$$$T = 4.8 s$$Therefore, it takes 4.8 s for the mass to make one complete revolution.

A 23 Kg Mass Is Connected to a Nail on a Frictionless