An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton ? Obtain the ratio of their speeds. (electron mass = $9.11 \times 10^{-31}$ kg, proton mass = $1.67 \times 10^{-27}$ kg, 1 eV = $1.60 \times 10^{-19}$ J).

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.

Answer the following : (d) In Fig. 6.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig. 6.13(ii), he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work done greater ?

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 ?

Answer the following :
(c) An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ?

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.

                                     

A family uses 8 kW of power. (b) Compare this area to that of the roof of a typical house.

State if each of the following statements is true or false. Give reasons for your answer.
(d) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey ? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is $10 \text{ m s}^{-1}$ ?

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

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:
(c) work done by friction on a body sliding down an inclined plane,

State if each of the following statements is true or false. Give reasons for your answer.
(c) Work done in the motion of a body over a closed loop is zero for every force in nature.

Underline the correct alternative :
(c) The rate of change of total momentum of a many-particle system is proportional to the...

The blades of a windmill sweep out a circle of area $A$. (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that $A = 30 \text{ m}^2$, $v = 36 \text{ km/h}$ and the density of air is $1.2 \text{ kg m}^{-3}$. What is the electrical power produced ?

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,

Underline the correct alternative :
(d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the...

Answer carefully, with reasons :
(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

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:
(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

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?