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__Page 147__**Solution 51**

Mass, m = 200 kg

Height, h = 2 m

Acceleration due to gravity, g = 9.8 m/s^{2}

i) Potential energy = m x g x h = 200 x 9.8 x 2 = 3920 J

ii) Work done is against gravity = Potential energy gained by the weights, therefore

Work done W = m x g x h = 200 x 9.8 x 2 = 3920 J**Solution 52**

(a) Work is done when a force applied on a body produces motion in it.

Formula for work done:

W = F x s

where W is the work done

F is force applied

S is the displacement of the body in the direction of force

(b) Mass of the person, m = 50 kg

Height of tower, h = 72 m

Acceleration due to gravity = 9.8 m/s^{2}

Work done W = m x g x h

= 50 x 9.8 x 72 = 35280 J**Solution 53**

(a) Work is said to be done when the force applied on a body produces motion in it.

Work done by a body in moving up is given by

W = m x g x h

where W is the work done against the gravity

m = mass of the body

g = acceleration due to gravity

h = height through which the body is lifted above the ground

(b) Force, F = 2 N

Distance, s = 10 cm = 0.1 m

Work done W = F x s = 2 x 0.1 = 0.2 J**Solution 54**

(a) When the displacement of a body is at right angles to the direction of foce acting on it, then work done is zero.

(b) Force, F = 50 N

Distance, s = 4 m

Angle between direction of force and direction of motion, θ = 60^{0}

**Solution 55**

(a) Energy is the ability to do work. SI unit of energy is Joule.

(b) Various forms of energy are:

1. Kinetic energy

2. Potential energy

3. Chemical energy

4. Heat energy

5. Light energy

6. Sound energy

7. Electrical energy

8. Nuclear energy

(c) Let masses of bodies be m

Velocity of one body, v_{1}= v

Velocity of another body, v_{2} = 2v

**Solution 56**

(a) The energy of a body due to its motion is called kinetic energy

(b) When the velocity becomes zero, the kinetic energy also becomes zero since kinetic energy is directly proportional to square of the velocity.

(c)

where m_{n} and m_{d} are the masses of horse and dog respectively.

**Solution 57**

(a) The energy of a body due to its position or change in its shape is known as its potential energy. E.g. a stretched rubber has potential energy due to change in its shape and water in the overhead tank has potential energy due to its height above the ground.

PE = m x g x h

where, PE is the potential energy of the body,

m is the mass of the body,

g is the acceleration due to gravity,

h is the height above the surface ofearth.

(b) Kinetic energy of a body is due to motion of the body while potential energy is due to position or change in shape of the body.

Kinetic energy is zero for a still body, while potential energy may or may not be zero for a still body.

Kinetic energy of a body is directly proportional to its speed while potential energy is directly proportional to the height to which the body is above the ground.

(c) Mass of ball, m = 0.5 kg

Speed v_{1} = 5 m/s

Speed v_{2} = 3 m/s

**Solution 58**

(a) The potential energy due to the position of the body above the ground is gravitational potential energy and the potential energy due to change in shape and size of the body is elastic potential energy. E.g. a stretched rubber has elastic potential energy due to change in its shape while water in the overhead tank has gravitational potential energy due to its height above the ground.

(b) Work done, W = 784 J

Mass, m = 20 kg

g = 9.8 m/s^{2}

W = m x g x h

784 = 20 x 9.8 x h

__Page 148__**Solution 71**

Work done is more on the bicycle because the truck does not move at all and the bicycle moves through a certain distance. And work is said to be done only when applied force produces motion in the body.

__Page 149__**Solution 72**

The work done will decrease as the angle between the direction of force and direction of motion is increased gradually because

W= F cos θ x s

and cos θ decreases as the angle θ is increased.

**Solution 73**

The work done will be zero when angle between the direction of force and direction of motion is 90^{o}because

**Solution 75**

The work done is zero because the gravitational force acts along the radius of the circular path, at right angles i.e. 90^{o} to the motion of satellite.**Solution 76**

Weight of man = Mg = 800 N

Weight of package = mg = 200 N

Total weight of man and package = Mg + mg = (M+m)g = 1000 N

Height of the summit, h = 1200 m

i) Work done = (M+m) x g x h = 1000 x 1200 = 12 x 10^{5} J

ii) Potential energy of the package = m x g x h = 200 x 1200 = 2.4 x 10^{5} J**Solution 77**

Potential energy becomes maximum.**Solution 78**

The work done by both X and Y are equal because irrespective of whether they reach the top of building by using a spiral or slanted ladder, the vertical distance moved by them against the gravity is same.**Solution 79**

Yes, the kinetic energy of the ball thrown inside a moving bus depends on the

speed of the bus because the speed of the bus adds up to the speed with which

the ball is thrown inside the moving bus.**Solution 80**

distance covered before stopping , s = 20 cm = 0.2 m

Here, initial velocity u = 400m/s

Final velocity = 0

Kinetic energy of the bullet is mainly converted into hear energy (by friction).

__Page 162__**Solution 1**

The commercial unit of energy is kilowatt-hour.**Solution 2**

One kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having power of 1 kilowatt is used for 1 hour.**Solution 3**

Megawatt and kilowatt are the units of power bigger than watt.**Solution 4**

1 watt is the power of an appliance which does work at the rate of 1 joule per second.**Solution 5**

1 horse power = 746 watt**Solution 6**

Power has watt as its physical unit**Solution 7**

1 watt**Solution 8**

Work done = 1200 J

Time taken = 2 minutes = 2 x 60 = 120 s

**Solution 9**

One kilowatt = 3.6 x 10^{6} J**Solution 10**

a) Power

b) Electrical Energy**Solution 11**

1 kW-h of electrical energy is commonly known as unit of electricity.**Solution 12**

A cell converts chemical energy into electrical energy.**Solution 13**

Electric motor**Solution 14**

a) Electric generator

b) Cell

c) Electric iron

d) Solar cell

e) Electric bulb**Solution 15**

a) Speaker

b) Steam engine

c) Car engine

d) Gas stove

e) Solar water heater**Solution 16**

a) Work

b) Joule ; second

c) kWh

d) conservation; transformed; created; destroyed

e) kinetic; potential

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