Answer :

Work done by a force f on a object which give body a displacement of d

where,

w is the work done on the object by force f

f is the force applied to the object

d is the displacement of the object after application of force

θ is the angle between force and displacement

A. The displacement of the bucket and the force applied on the bucket by the man have the same direction i.e. θ=0. Hence, the work done by a man is positive and the work is done on the bucket.

⇒ (∵ cos 0^{0}=1)

Hence, work done is positive.

B. The gravitational force acts downwards on the bucket. But the displacement of the bucket is upwards i.e. θ=180. Hence, the work done is negative and θ=180

(∵ cos 180^{0}=-1)

Hence, work done is negative.

C. Frictional force always acts opposite to the direction of motion of object i.e. θ=180. Hence, work done by frictional force is always negative.

(∵ cos 180^{0}=-1)

Hence, work done is negative.

D. In this case, frictional force acts on the body due to the roughness of the horizontal plane in a direction opposite to the direction of motion. To obtain a uniform velocity, a uniform force must be applied in the direction of motion i.e. θ =0. Hence, the work done by the force is positive.

⇒ (∵ cos 0^{0}=1)

Hence, work done is positive.

E. The resistive force always acts in the direction opposite to that of the motion of pendulum to bring the pendulum to rest i.e. θ =180. Hence, the work done by the resistive force is negative.

(∵ cos 180^{0}=-1)

Hence, work done is negative.

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