A mass of 1 kg is attached to the lower end of a string 1 m long whose upper end is fixed . The mass is made to rotate in a horizontal circle of radius 60 cm . if the circular speed of the mass is constant , find the tension in the string and the period of motion .
Given ,
Mass of object (m) = 1kg
Length of string (l) = 4m
Radius of circle (r) = 60cm
Tension on the string (T) = ?
Period of motion = ?
From figure ,
Tsinθ = mv2/r
Tcosθ =mg
tanθ = v2/rg and
sinθ = r/l = 0.6/1 = 0.6
or , θ = sin-1(0.6) = 36.87
so from relation
Tcosθ =mg
T = mg/cosθ =1×10/cos36.87 = 12.5 N
Again , from relation
tanθ = v2/rg
or , t = 2π√lcosθ/g
= 2π√1xcos36.87/10 = 1.78s