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. t = 0.25 s
C. t = 2 s
D. t = 1 s

Answer

D

Explanation

According to question, torque, `tau=l alpha`
`because" "tau=0`
Its means that, `alpha=0, alpha=(d^(2)theta)/(dt^(2))`
`"Given, "theta(t)=2t^(3)-6t^(2)`
`"So, "(d theta)/(dt)=6t^(2)-12t`
`rArr" "(d^(2)theta)/(dt)=12t-12" "(because alpha=(d^(2)theta)/(dt^(2))=0)`
`12t-12=0 and t=1s`