Question

A 24 kg mass is connected to a nail on a frictionless table by a massless string 1.1 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 54 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? (Give answer to the nearest 0.1 s)

Answer 1

Time take for the mass to make one complete revolution which is given as :

using an equation,       T = m v² / r                                                              { eq.1 }

orbital time-period may be defined as,    t = 2r / v

or v = 2r / t                                                                                         { eq.2 }

then, we have T = m (2r / t)² / r

T = 4² m r / t²

t² = 4² m r / T

t = 2m r / T                                                                                    { eq.3 }

where, m = mass of the object = 24 kg

r = distance between object & table = 1.1 m

T = tension in the string = 54 N

inserting these values in eq.3,

t = 2(24 kg) (1.1 m) / (54 N)

t = 20.488 s²

t = 2 (3.14) (0.698 sec)

t = 4.38 sec