Question

A string of length 0.5m carries a Bob of mass 0.1kg at its end. If this is to be used as a conical pendulum of period 0.4π sec,calculate the angle of inclination of the string. with the vertical and the tension in the string?​

Answer 1

answer is attachment hope this help you

Answer 2

Given:

The length of the string (l) = 0.5m

The mass of the bob (m) = 0.1 kg

The time period of the pendulum (t) = 0.4π s

To Find:

1) The angle of inclination of the string with the vertical (∅)

2) The tension in the string (T)

Solution:

The angle of inclination of the string with the vertical is 37° and the tension in the string is 1.25 N.

A conical pendulum is similar to a simple pendulum in construction but different in the movement of the bob.

In a simple pendulum, the bob moves to-and-fro while in a conical pendulum, it moves in a circle.

For a conical pendulum inclined with the vertical at ∅,

The time period = 2π √(l cos∅ / g)

Substituting the values,

0.4π = 2π √(l cos∅ / g)

or 0.2 = √(l cos∅ / g)

Squaring both the sides,

4 / 100 = l cos∅ / g

Taking g = 10 m/s²,

4 / 10 = 0.5 cos∅

or cos∅ = 4 / 5

or ∅ = 37°

The vertical component of the tension T gives the required centripetal force,

⇒ T cos∅  = mg

or T = 0.1 X 10 X 5 / 4

= 5 / 4

= 1.25 N