It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass \(1.00\) g falling from a height of \(1.00\) km. It hits the ground with a speed of \(50.0\) m/s. Work done by the gravitational force and work done by the unknown resistive force respectively are:

A body is moved quasi-statically from point \(A\) to point \(C\) in a uniform gravitational field. During the motion, a constant vertical upward force \(F\) of magnitude \(mg\) is applied to keep the body in equilibrium. The body is moved either directly along the inclined path \(AC\) or along the path \(A \rightarrow B\rightarrow C,\) as shown in the figure. If \(W_{AC}\)​ and \(W_{ABC}\)​ denote the work done by the applied force \(F\) along the two paths, respectively, then:

1. \(W_{AC}=W_{ABC}\)
2. \(W_{AC}>W_{ABC}\)
3. \(W_{AC}<W_{ABC}\)
4. None of the above

A \(500 ~\text{kg}\) object slides across a horizontal surface where the coefficient of kinetic friction is \(\mu=0.7.\) To maintain a constant velocity of \(10~\text{m/s},\) an external force is applied horizontally in the direction of motion. The object travels a total distance of \(4~\text{km}\) under these conditions. The work done by the external force is:
 1. \(3.5 \times 10^6~\text{J} \)
2. \(28 \times 10^6~\text{J} \)
3. \(7 \times 10^6 ~\text{J} \)
4. \(14 \times 10^6 ~\text{J} \)

A \(2\) kg particle moves along \(x\)-axis such that its position \((x)\) varies with time \((t)\) as \(x = 2t^{2}+3. \) During the initial \(5\) s, the work done by all the forces acting on the particle is:
1. \(400\) J
2. \(500\) J
3. \(600\) J
4. \(900\) J

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled \(3~\text{m}\) is:

1. \(2.5~\text{J}\)
2. \(6.5~\text{J}\)
3. \(4~\text{J}\)
4. \(5~\text{J}\)

A constant force acts on a body of mass \(1\) kg, providing it a kinetic energy of \(1800~\text{J}\) by the end of \(5^{\mathrm{th}}\) second. If the body was initially at rest, at the beginning of the action of force, then the magnitude of the force is equal to: