Underline the correct alternative :
(a) When a conservative force does positive work on a body, the potential energy of the body...

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

The blades of a windmill sweep out a circle of area $A$. (b) What is the kinetic energy of the air ?

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

The blades of a windmill sweep out a circle of area $A$. (a) If the wind flows at a velocity $v$ perpendicular to the circle, what is the mass of the air passing through it in time $t$ ?

A pump on the ground floor of a building can pump up water to fill a tank of volume $30 \text{ m}^3$ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump ?

A body of mass 0.5 kg travels in a straight line with velocity $v = ax^{3/2}$ where $a = 5 \text{ m}^{-1/2} \text{ s}^{-1}$. What is the work done by the net force during its displacement from $x = 0$ to $x = 2$ m ?

Underline the correct alternative :
(b) Work done by a body against friction always results in a loss of its...

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following (Fig. 6.14) is a possible result after collision ?

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of $0.05 \text{ kg s}^{-1}$. What is the speed of the trolley after the entire sand bag is empty ?

Given in Fig. 6.11 are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

                                     

The bob $A$ of a pendulum released from $30^{\circ}$ to the vertical hits another bob $B$ of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob $A$ rise after the collision ? Neglect the size of the bobs and assume the collision to be elastic.

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(b) work done by gravitational force in the above case,

A family uses 8 kW of power. (a) Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square meter. If 20% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?

A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the
(d) change in kinetic energy of the body in 10 s,
and interpret your results.

State if each of the following statements is true or false. Give reasons for your answer.
(b) Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance ?

A body constrained to move along the z-axis of a coordinate system is subject to a constant force $F$ given by $F = (-\hat{i} + 2\hat{j} + 3\hat{k}) N$ where $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. (b) Fat supplies $3.8 \times 10^7 \text{J}$ of energy per kilogram which is converted to mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
(d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,