energy and kinetic energy (lec 2)

 video lectures for energy and kinetic energy

Question 1: What is the relation between momentum and kinetic energy?

Question 2: State work energy theorem.

Question 3: Two bodies of masses m and 4m are moving with

equal kinetic energy. The ratio of the velocities with

which they are travelling is _______.

(a) 1 : 2  

(b) 2 : 1

(c) 3 : 4  

(d) 4 : 5

Question 4: The momentum `‘P’` and kinetic energy `‘E’` of a body

of mass `‘m’` are related as

(a) `P = \sqrt{2mE}` 

(b) `P = \frac{1}{2}mE`

(c)  `P =\frac{2m}{E}`

(d) P = 2mE

 

Question 5: If the momentum of a moving bus with constant mass is doubled, then its kinetic energy becomes ______. (a) double (b) triple (c) quadruple (d) remains constant

Question 6: Which one of the following is not the unit of energy?

(a) joule

(b) newton metre

(c) kilowatt

(d) kilowatt hour

Question 7: The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

Question 8: A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

Question 9: The kinetic energy of an object of mass m moving with a velocity of `5 ms^{-1}` is `25 j`. If this velocity is double, then what will be it's kinetic energy?

a) `50 J`

b) `250 J`

c) `200 J`

d) `100 J`

Question 10: A force acting on a mass of `20 kg` changes its velocity from `5ms^{-1}` to `2ms^{-1}`. Calculate the work done by the force.

a) `210 J`

b) `-210 J`

c) `110 J`

d) `-120 J`

Question 11: A body of mass m is moving with a constant velocity. How much work must be done on the body to bring it to rest `V` Will you come?

Question 12: Calculate the work to be done to stop a car of mass `1500 kg` which is moving with a velocity of `60 kmh^{-1}`.

a) `208 KJ`

b) `208 J`

c) `108 KJ`

d) `106 KJ`

Question 13: A freely falling body eventually stops on reaching the ground. What is the measure of its kinetic energy? 

Question 14: A horse and a dog are running at the same speed. If the weight of the horse is ten times that of the dog, then its kinetic energy, What will be the ratio?

a) `10 : 1`

b) `1 : 10`

c) `1 : 1`

d) `2 : 1`

Question 15: An object of mass `2 kg` starts falling from rest. What will be Its kinetic energy when  falls down after `2` seconds?(` g=10ms^{-2}`)

a) `200 J`

b) `800 J`

c) `400 J`

d) `100 J`

Answer Key

Q1 Answer: Kinetic energy `E` and momentum `P` are related as `P=2mE`

Q2 Answer: the total work done by the sum of all the forces acting on a particle is equal to the change in the kinetic energy of that particle.

Q3  (b),  Q4   (a),   Q5   (c),

Q6   (c) Kilowatt is the unit of power, not of energy.

Q7  Solution: Let the body covers a distance s when a constant force F is applied in the direction of motion.

Work done by this force, `W=F . s`

Let the velocity of object of mass m change

from u to v with acceleration a on application

of constant force F, then `F = ma`

From equation of motion, `v^{2}-u^{2}= 2as`, we get

`s= \frac{v^{2}-u^{2}}{2a}`

∴`W=Fs=ma(\frac{ v^{2}-u^{2}}{2a})`

`=\frac{1}{2}mv^{2}-\frac{1}{2}m u^{2}`

= final kinetic energy – initial kinetic energy

= change in kinetic energy

Q8   Solution:

Let m and `M` be the masses of a light and a heavy object moving with velocities `v`and `V` respectively.

As both have the same momentum,

`∴ mv = MV`

or `\frac{M}{V} …(i)`

Kinetic energy of light object,

`K_{m}=\frac{1}{2}mv^{2}`

Kinetic energy of heavy object,

`K_{m}=\frac{1}{2}mV^{2}`

Kinetic energy of heavy object,

`K_{M}=\frac{1}{2}MV^{2}`

`\frac{K_{m}}{K_{M}}=\frac{\frac{1}{2}mv^{2}}{\frac{1}{2}MV^{2}}`

`=\frac{m}{M}.\frac{v^{2}}{V^{2}}`

`=\frac{m}{M}(\frac{M}{m})^{2}=\frac{M}{m}....`      Using (1)

As  `M>m`;

`K_{m} > K_{M}`, i.e. light object has larger kinetic energy.

Q9    (d),   Q10   (b),   

Q11   solution:

mass `= m`

Velocity `= V`

`E_{k}=\frac{1}{2}mv^{2}`

The initial kinetic energy of the material is `\frac{1}{2}mv^{2}`. Hence, the same amount of work (`frac{1}{2}mv^{2}`) has to be done to bring it to rest.

Q12   (a),

Q13  Answer:- When a freely falling body reaches the ground and stops, then its kinetic energy gets converted into other types of energy. This can generate heat energy, sound energy and light energy. Finally it is transferred to potential energy.

Q14   (a),  Q15   ©.