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

Options

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

Answer

A

Explanation

Given : 0 `(t) = 2 t^(3) 6t^(2) , (d theta)/(dt) = 6t^(2) - 12 t`
Angular acceleration , `alpha = (d^(2) theta)/(dt^(2)) = 12 t -12`
When angular acceleration `(alpha)` is zero , then the torque on the wheel becomes zero `(because tau = I alpha)`
`implies 12 t - 12 = 0` or `t = 1` s