1. Use the sign of work

Work done by a force is $W = \vec F \cdot \vec s = Fs\cos\theta$ It is:

• positive if force and displacement are in the same direction,
• negative if they are in opposite directions,
• zero if they are perpendicular.

Now evaluate each statement.

2. Statement A

Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.

While lifting, the bucket moves upward. The man applies an upward force through the rope. Thus force and displacement are in the same direction.

So, $W_{\text{man}} > 0$ Hence A is false.

3. Statement B

Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

During lifting, displacement of bucket is upward, but gravitational force acts downward. Thus force and displacement are opposite.

So, $W_g = -mgh < 0$ Hence B is true.

4. Statement C

Work done by friction on a body sliding down an inclined plane is positive.

If a body slides down the incline, friction acts up the incline, opposite to motion. Therefore friction does negative work: $W_f < 0$ Hence C is false.

5. Statement D

Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.

On a rough horizontal plane with uniform velocity, net force is zero, so applied force equals friction in magnitude. But the body is moving in the direction of the applied force, so applied force does positive work. Friction does equal negative work, making net work zero, not the applied force’s work.

Thus, $W_{\text{applied}} > 0$ Hence D is false.

6. Statement E

Work done by the air resistance on an oscillating pendulum is negative.

Air resistance always opposes the motion of the pendulum bob. Therefore its work is negative.

So, $W_{\text{air resistance}} < 0$ Hence E is true.

7. Collect the correct statements

Correct statements are: $\boxed{B \text{ and } E}$

This corresponds to Option D.

8. Comparison with stored answer

Stored correct answer: D

Our derived answer: D

So they agree.