A constant external torque acts for a very brief $\Delta t$ on a rotating system having moment of inertia I.

Question

1) the angular momentum of the system will change by $\large\frac{z \Delta t}{I}$

2) the angular velocity of the system will change by $\large\frac{z \Delta t}{I}$

3) if the system was initially at rest, it well acquire kinetic energy $\large\frac{(z \Delta t)^2}{2I}$

4) the kinetic energy of the system will change by $\large\frac{(z \Delta t)^2}{I}$

Which of the following is correct?

a) 1,2 and 3

b) 2,3 and 4

c) 1,3 and 4

d) 1,2 and 4