|
Response Details:
Mass of the bob, M = 0.055 kg
Length of the string , L = 0.6 m
Circumference , C = 0.88 m
Radius of the circular path = R
Tension in the string = T
Angle made by the string with horizontal = θ
Circumference , C = 2 π R
Radius, R = C / 2 π
= 0.88 / ( 2 * 3.14 )
= 0.14 m
From the figure, Cos θ = Adjacent side to θ / hypotenuse
= R / L
= 0.14 / 0.6
= 0.2333
θ = arc cos 0.2333
= 76.51 degrees
In vertical direction , T sin θ = M g .............(1)
In horizontal direction, T cos θ = M ω2 R ..............(2)
(a)
from equ. (1)
Tension in the string, T = M g / sin θ
= 0.055 * 9.8 / 0.9724
= 0.5543 N
(b)
From equ (2)
T cos θ = M ω2 R
0.5543 * 0.2333 = 0.055 * ω2 * 0.14
Angular velocity, ω = 4.1 rad / s
Time period, T = 2π / ω
= 2 * 3.14 / 4.1
= 1.53 s
|