A body moves from a position $r_1=\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}-4\hat{\mathrm{k}}\right) \mathrm{m}$ to a position, $r_2=(3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+5\hat{\mathrm{k}}) \mathrm{m}$ under the influence of a constant force $F=\left(4\hat{\mathrm{i}}+\hat{\mathrm{j}}+6\hat{\mathrm{k}}\right) \mathrm{N}$. The work done by the force is

Assertion $\left(A\right)$ : The work done by the electrostatic force is zero when a point charge moves in a circular path around another charge.

Reason $\left(R\right)$ : The dot product of force and displacement vectors gives work done.

The diagram shows a barrel of weight $1.0\times {10}^3 \mathrm{N}$ on a frictionless slope inclined at $30°$ to the horizontal.

The force is parallel to the slope. Whet is the work done in moving the barrel a distance of $5.0 \mathrm{m}$ up the slope?

Identify the correct statements from the following:

(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

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

(C) Work done by friction on a body sliding down an inclined plane is positive

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

(E) Work done by the air resistance on an oscillating pendulum is negative

Choose the correct answer from the options given below:

A lawn roller has been pushed through a distance of $80 \mathrm{m}$ by applying a force of $50 \mathrm{kg}.$wt in a direction inclined at $60°$ with the ground. Calculate the work done on the roller.