Consider a torque ⃗τ that is constant in both magnitude and direction, and acts on a rigid body of mass 10 kg at a point 1 m from the pivot.

How much work does the torque do on the rigid body, if it turns through an angle of 180◦ while the torque is acting? Assume the acceleration due to gravity is 10 m/s2.

1. 180 N ·
m 2. 100 N ·
m 3. 180 τ
4. π τ
5. We need the rotational inertia of the body.
6. Zero
7. 50 N · m 8. 200 N · m

the answer is pi t , number 4.

Hmm...let me think about this one for a second.

Ah, I've got it! The work done by the torque can be found using the equation:

Work = Torque x Angular Displacement

In this case, the magnitude of the torque is constant, and it's acting on the rigid body as it turns through an angle of 180 degrees. So, the work done would be:

Work = (Magnitude of Torque) x (Angular Displacement)

Now, we're given that the magnitude of the torque is constant, but no specific value is given. So, unfortunately, we can't calculate the exact work done without that information.

Therefore, the correct answer would be option 5. We need the rotational inertia of the body. Without that information, we can't determine the amount of work done by the torque.

To find the work done by the torque on the rigid body, we can use the formula:

Work = Torque * Angle

In this case, the torque is constant in magnitude and direction, so we can calculate the work done as:

Work = Magnitude of Torque * Angle

We are given that the magnitude of the torque is constant, so we don't need the rotational inertia of the body. We are also given that the angle through which the rigid body turns is 180°.

Substituting the given values, we have:

Work = Magnitude of Torque * Angle
= Magnitude of Torque * 180°

Now, the magnitude of the torque is not given, so we cannot find the exact value for the work done. Therefore, options 1, 3, 4, 5, 6, and 7 are incorrect.

The correct option is 8. 200 N · m, as this represents the work done by the torque.

To calculate the work done by a torque on a rigid body, we can use the formula:

Work = torque x angle of rotation

In this case, the torque is constant in magnitude and direction, so we don't need to consider the angle of rotation.

The formula for torque is:

Torque = force x lever arm

The lever arm is the perpendicular distance from the pivot point to the line of action of the force. In this case, the lever arm is 1 m.

We know that the force causing the torque is due to gravity acting on the mass of the rigid body. The force can be calculated using the formula:

Force = mass x acceleration due to gravity

Given that the mass of the body is 10 kg and the acceleration due to gravity is 10 m/s², we can calculate the force:

Force = 10 kg x 10 m/s² = 100 N

Now we can substitute the values into the torque formula:

Torque = force x lever arm = 100 N x 1 m = 100 N·m

Finally, we can calculate the work done by the torque:

Work = torque x angle of rotation = 100 N·m x 180° = 18000 N·m

Therefore, the work done by the torque on the rigid body, as it turns through an angle of 180°, is 18000 N·m.

So, the correct answer is option 8: 18000 N·m.