A force $F$ acting on an object varies with distance $x$ as shown here. The force is in $\mathrm{N}$ and $x$ in $\mathrm{m}$. The work done by the force in moving the object from $x=0$ to $x=6 \mathrm{m}$ is

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.

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:

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.

A block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $\mu$ and compresses a spring of spring constant $k$ by a distance $x$  before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$.

Then