Question

A particle of mass 1 kg is suspended from a ceiling
through a string of length 10root2 m. The particle
moves in a horizontal circle. Find its time period.
(1) 2pi sec (2) pi sec (3) pi/2 sec
(4) 1 sec​

Answer 1

Given info : A particle of mass 1 kg is suspended from a ceiling  through a string of length 10root2 m. The particle  moves in a horizontal circle.

To find : the time period is ..

solution : at equilibrium,

tension in string along horizontal direction = mω²r

⇒ Tsin45° = mω²r ...(1)

tension in string along vertica direction = mg

⇒ Tcos45° = mg ...(2)

equations (1) and (2) we get,  tan45° = ω²r/g

⇒ ω² = gtan45°/r = (10 × 1)/10 = 1

r = lsin45° = 10√2 × 1/√2 = 10 m

⇒ ω = 1 rad/s

⇒ 2π/T = 1 rad/s

⇒ T = 2π

therefore the time period of the particle is 2π sec. hence option (1) is correct choice.