A conical pendulum has a string of length 95cm and a bob of mass 150g. It describes a circle of radius 25cm in horizontal plane when sets into motion. the period of rotation is ?

1
by durgaSetty55

2015-09-21T16:58:44+05:30

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Angle that the string makes with the vertical line = Ф
tan Ф = R / L      ---- (1)
R = radius of horizontal circle
L = length of string            m = mass of pendulum bob
ω =  angular velocity of rotation of bob

balancing the forces, as the pendulum is in uniform motion in a circle.  There is no acceleration in vertical direction.  T is the tension i n the string.

T CosФ = m g      and T sinФ = centripetal force = m R ω²
=>   tan Ф =  m R ω² / m g
using (1) we get:   ω² = g / L

time period = 2 π / ω = 2 π √ (L/g)

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