Question

a 20 cm wide thin circular disc of mass 200 g is suspended to a rigid support from a thin metallic string by holding the rim of the disc the string is twisted through 60° and released it namaskar w performed angular oscillation of period 1 second calculate the maximum restoring torque generated in the string under u damped condition​

Answer 1

Given that,

Thickness of disc = 20 cm

Mass of disc = 200 g

Angle = 60°

Time period = 1 sec

We need to calculate the length of string

Using formula of time period

$T=2\pi\sqrt{\dfrac{L}{g}}$

$L=\dfrac{T^2\times g}{4\pi^2}$

Put the value into the formula

$L=\dfrac{1^2\times9.8}{4\times3.14^2}$

$L=0.248\ m$

We need to calculate the maximum restoring torque generated in the string

Using formula of torque

$\tau=-Lmg\sin\theta$

Where, l = length of the string

m = mass of disc

$\theta$ = twist angle

Put the value into the formula

$\tau=-0.248\times200\times10^{-3}\times9.8\sin60$

$\tau=-0.421\ N-m$

Negative sign shows the opposite direction of torque

Hence, The maximum restoring torque generated in the string is 0.421 N-m.