The instantaneous angular position of a point on a rotating wheel is given by the equation
`theta(t) = 2t^(3) - 6 t^(2)`
The torque on the wheel becomes zero at

Options

A. t =0.5 s
B. 1 = 0.25 s
C. t = 2 s
D. t = 1 s

Answer

D

Explanation

(d) The instantaneous angular position of a point on a rotating wheel is given by the equation `theta(t) = 2 t^3 - 6 t^2`
According to question, torque, `tau = 0`
its means that, `prop = 0`
`prop = (d^2 theta)/(dt^2)`
Given `theta(t) = 2t^3 - 6 t^2`
So, `(d theta)/(dt) = 6 t^2 - 12 t`
`(d^2 theta)/(dt^2) = 12t - 12` `(because prop = (d^2 theta)/(dt^2) = 0)`
`12 t - 12 = 0`
`t = 1 s`.