Work Done by Torque on Square Plate of Mass M

[1/2"]

Homework Statement

In the figure shown a square plate of mass M and side of length L
is fixed at the center . The force F makes the square plate rotate.
The force is always perpendicular to the side.
Find the work done by the force.

Homework Equations

Work = torque x θ

The Attempt at a Solution

I considered the moment arm to be half of the diagonal of length L/√2
Then the force acting perpendicular to it will be F/√2
Torque =FL /2 but then how do i find the angle covered?
The book's answer is (3F²t²)/M

 

[azizlwl]

Homework Statement

In the figure shown a square plate of mass M and side of length L
is fixed at the center . The force F makes the square plate rotate.
The force is always perpendicular to the side.
Find the work done by the force.

Homework Equations

Work = torque x θ

The Attempt at a Solution

I considered the moment arm to be half of the diagonal of length L/√2
Then the force acting perpendicular to it will be F/√2
Torque =FL /2 but then how do i find the angle covered?
The book's answer is (3F²t²)/M

There is t in the solution but is not stated in the question.

 

[voko]

The torque is constant, so the the angular acceleration is constant. So you can obtain it as a function of time.

 

[1/2"]

The torque is constant, so the the angular acceleration is constant. So you can obtain it as a function of time.

Can please be more elaborate ?
I reaaly appreciated your help,Thanks.

 

[voko]

I am not sure what else I could say without solving the entire problem. What is the equation relating angular acceleration and torque?