Answer
In situation (3) when $~~l=2,~~$ the net torque on the particle is zero.
Work Step by Step
We can write a general equation for the net torque:
$\tau = \frac{dl}{dt}$
We can find an expression for the net torque in each case:
(1) $l = 3t+4$
$\tau = \frac{dl}{dt} = 3$
(2) $l = -6t^2$
$\tau = \frac{dl}{dt} = -12t$
(3) $l = 2$
$\tau = \frac{dl}{dt} = 0$
(4) $l = \frac{4}{t}$
$\tau = \frac{dl}{dt} = -\frac{4}{t^2}$
In situation (3) when $~~l=2,~~$ the net torque on the particle is zero.
