# Work and energy : NCERT Intext Questions Page 148

Q.1 ¬† ¬† A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let¬†us take it that the force acts on the object through the displacement. What is the work done in this case?
¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬†¬†

Sol.¬† ¬† ¬†When a force F acts on an object to displace it through a distance S in its direction,
¬† ¬† ¬† ¬† ¬† ¬†then the work done W on the body by the force is given by:
¬† ¬† ¬† ¬† ¬† ¬†Work done = Force √ó Displacement
¬† ¬† ¬† ¬† ¬† ¬†W = F √ó S
¬† ¬† ¬† ¬† ¬† ¬†Where,
¬† ¬† ¬† ¬† ¬† ¬†F = 7 N
¬† ¬† ¬† ¬† ¬† ¬†S = 8 m
¬† ¬† ¬† ¬† ¬† ¬†Therefore, work done, W = 7 √ó 8
¬† ¬† ¬† ¬† ¬† ¬†= 56 Nm
¬† ¬† ¬† ¬† ¬† ¬†= 56 J

Page 149

Q.1 ¬† ¬†When do we say that work is done?
Sol.¬† ¬† ¬†Work is done whenever the given conditions are satisfied:
¬† ¬† ¬† ¬† ¬† ¬†(i) A force acts on the body.
¬† ¬† ¬† ¬† ¬† ¬†(ii) There is a displacement of the body caused by the applied force along the direction of the applied¬†force.

Q.2 ¬† ¬† Write an expression for the work done when a force is acting on an object in the direction of its¬†displacement.
Sol. ¬† ¬† When a force F displaces a body through a distance S in the direction of the applied force, then the work¬†done W on the body is given by the expression:
¬† ¬† ¬† ¬† ¬† ¬†Work done = Force √ó Displacement
¬† ¬† ¬† ¬† ¬† ¬†W = F √ó s8080

Q.3 ¬† ¬†¬†Define 1 J of work.
Sol.¬† ¬† ¬† ¬† ¬†1 J is the amount of work done by a force of 1 N on an object that displaces it through a distance of 1 m in¬†the direction of the applied force. 80

Q.4 ¬† ¬† A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much¬†work is done in ploughing the length of the field?
Sol. ¬† ¬† Work done by the bullocks is given by the expression:
¬† ¬† ¬† ¬† ¬† ¬†Work done = Force √ó Displacement
¬† ¬† ¬† ¬† ¬† ¬†W = F √ó d
¬† ¬† ¬† ¬† ¬† ¬†Where,
¬† ¬† ¬† ¬† ¬† ¬†Applied force, F = 140 N
¬† ¬† ¬† ¬† ¬† ¬†Displacement, d = 15 m
¬† ¬† ¬† ¬† ¬† ¬†W = 140 √ó 15 = 2100 J
¬† ¬† ¬† ¬† ¬† ¬†Hence, 2100 J of work is done in ploughing the length of the field.

¬†Page 152

Q.1 ¬† ¬†¬†What is the kinetic energy of an object?
Sol. ¬† ¬† ¬†Kinetic energy is the energy possessed by a body by the virtue of its motion. Every moving object¬†possesses kinetic energy. A body uses kinetic energy to do work. Kinetic energy of hammer is used in¬†driving a nail into a log of wood, kinetic energy of air is used to run wind mills, etc.

Q.2 ¬† ¬† Write an expression for the kinetic energy of an object.
Sol.¬† ¬† ¬† If a body mass m is moving with a velocity v, then its kinetic energy ${E_k}$ is given by the expression,¬†
¬† ¬† ¬† ¬† ¬† ¬†${E_k} = {1 \over 2}m{v^2}$.
¬†Its SI unit is Joule (J).

Q.3 ¬† ¬† The kinetic energy of an object of mass, m moving with a velocity of 5 m s‚ąí1 is 25 J.What will be its¬†kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased¬†three times?
Sol. ¬† ¬†¬† ¬† ¬†Expression for kinetic energy ${E_k} = {1 \over 2}m{v^2}$
¬† ¬† ¬† ¬† ¬† ¬† m = Mass of object¬†
¬† ¬† ¬† ¬† ¬† ¬† v = Velocity of the object¬†$m{s^{ - 1}}$
¬† ¬† ¬† ¬† ¬† ¬† Given that kinetic energy,¬†${E_k} = 25J$

¬† ¬† ¬† ¬† ¬† ¬† (i) If the velocity of an object is doubled, then v = 5 √ó 2 = 10 $m{s^{ - 1}}$.
¬† ¬† ¬† ¬† ¬† ¬† Therefore, its kinetic energy becomes 4 times its original value, because it is proportional to the square¬†of the velocity. Hence, kinetic energy = 25 √ó 4 = 100 J.
¬† ¬† ¬† ¬† ¬† ¬† (ii) If velocity is increased three times, then its kinetic energy becomes 9 times its original value, because¬†it is proportional to the square of the velocity. Hence, kinetic energy = 25 √ó 9 = 225 J.80

Page 156

Q.1 ¬† ¬†¬†What is power?
Sol. ¬† ¬† Power is the rate of doing work or the rate of transfer of energy. If W is the amount of work done in time¬†t, then power is given by the expression,
¬† ¬† ¬† ¬† ¬† ¬†$Power = {{Work} \over {Time}} = {{Energy} \over {Time}}$
¬† ¬† ¬† ¬† ¬† ¬†$P = {W \over T}$
¬† ¬† ¬† ¬† ¬† ¬†It is expressed in watt (W).

Q.2 ¬† ¬† Define 1 watt of power:
Sol.¬† ¬† ¬† ¬† ¬†¬†A body is said to have power of 1 watt if it does work at the rate of 1 joule in 1 s,i.e.,
¬† ¬† ¬† ¬† ¬† ¬†$1W = {{1J} \over {1s}}$

Q.3 ¬† ¬† A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
Sol.¬† ¬† ¬†Power is given by the expression,
¬† ¬† ¬† ¬† ¬† ¬†$Power = {{Work\,done} \over {Time}}$
¬† ¬† ¬† ¬† ¬† ¬†Work done = Energy consumed by the lamp = 1000 J¬†
¬† ¬† ¬† ¬† ¬† ¬†$Power = {{1000} \over {10}} = 100J{s^{ - 1}}$
¬† ¬† ¬† ¬† ¬† ¬†= 100 W¬†

Q.4 ¬† ¬† Define average power.
Sol.¬† ¬† ¬†A body can do different amount of work in different time intervals. Hence, it is better to deŌźine average¬†power. Average power is obtained by dividing the total amount of work done in the total time taken to do¬†this work.
¬† ¬† ¬† ¬† ¬† ¬†$Average\,\,Power = {{Total\,work\,done} \over {Total\,time\,taken}}$

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