Zigya Logo

Chapter Chosen

Work, Energy and Power

Book Chosen

Physics Part I

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
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 m s–1?
 

Given, 

Radius of the rain drop, r = 2 mm = 2 × 10–3 m

Volume of the rain drop, V = 4 over 3πr3

                                   = 4 over 3 × 3.14 × (2 × 10-3)3 m-3
Density of water, ρ = 103 kg m–3
 

Mass of the rain drop, m = ρ

                                 = 4 over 3 × 3.14 × (2 × 10-3)3 × 103 kg
Gravitational force, F = mg

                            =  4 over 3× 3.14 × (2 × 10-3)3 × 103 × 9.8  N
The work done by the gravitational force on the drop in the first half of its journey, 

                        WI = F . s 

                             =4 over 3 × 3.14 × (2 × 10-3)3 × 103 × 9.8 × 250
                             =  0.082 J 

This amount of work is equal to the work done by the gravitational force on the drop in the second half of its journey.


i.e., 
WII = 0.082 J 

According to the law of conservation of energy,

If no resistive force is present, then the total energy of the rain drop will remain the same. 

∴ Total energy at the top, 

     ET = mgh + 0 

         = (4/3) × 3.14 × (2 × 10-3)3 × 103 × 9.8 × 500 × 10-5 

          = 0.164 J 

Due to the presence of a resistive force, the drop hits the ground with a velocity of 10 m/s.

∴Total energy at the ground is, 

      EG = (1/2) mv2 + 0 

           = (1/2) × (4/3) × 3.14 × (2 × 10-3)3 × 103 × 9.8 × (10)

           = 1.675 × 10-3 J 

∴ Resistive force = E– ET = –0.162 J
164 Views

Is work a scalar or a vector quantity?

Work is dot product of two vectors. i.e. F with rightwards arrow on top times S with rightwards arrow on top.

And dot product is a scalar quantity. Therefore, work is a scalar quantity. 
1450 Views

Define watt.

Power is said to be one watt if one joule of work is done in one second. 
860 Views

Define the unit joule.

Work done is said to be one joule if one newton of  force displaces the body through a distance of one meter in the direction of applied  force .
799 Views

What is watt?

SI unit of power is Watt. 
773 Views

What are different units of energy?

The different units of energy are :

(i) Joule            
(ii) Erg
(iii) eV            
(iv) KWh
(v) Calorie.

804 Views