# Different types of work done, Definition, Units and Dimension

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Hello, friends for various competitive exams like RRB NTPC, ALP, SSC,  CDS, and UPSC general science is a vital subject. In this post, we covered a little portion of the chapter Work Power and Energy.  Here we have provided notes on “Different types of work done, definition, dimensions, and formulas of work.

## Introduction

• Usually, doing something in our daily life is called work. For example, Reading books, writings notes for competitive exams, listening to music, painting a beautiful landscape, etc. All are said to be working. But the definition of work in physics is not so simple. The definition of Work in physics is defined by some formula or some numerical values.

## Definition of Work

• In Physics the “work” is defined as the dot product or scalar product of the component of the force in the direction of the displacement and displacement .

• Work (W) = f Vector . d vector [F= force, d=displacement ]

• Or, W= (f Cos θ) d [f Cos θ = The component of the force in the direction of the displacement]

• Or,  W=fd Cos θ
• Here Theta is the angel between the the direction of force and displacement.
Value of work will be maximum at θ=0 deg and minimum at θ=90deg.

## “Is work a Vector or Scalar?”

The ‘Work’ is a Scalar quantity.
• We Known the formula of Work That is W=fdCos θ. Here both the force and displacement are vector quantity that means both the quantity have magnitude and direction. And the dot product or Scalar product of two vector quantity always a Scalar quantity.

• In other words the work done is just nothing but the energy generated by an external force. Work has only a magnitude but no direction. Therefore, work is a scalar quantity.

## Unit of Work

• The SI unit of Work is joule (J) and the CGS unit of Work is Erg .
• The unit Joule named after the famous British physicist James Prescott Joule.

• The joule is a derived unit of energy in the International System of Units.
It is equal to the work done on an object when a force of one newton acts on that object in the direction of the force’s motion through a distance of one metre (1 newton-metre or N⋅m).

The unit of Force is Newton (N) and the unit of Displacement is Metre (m), so the unit of force is Newton (N) . Metre (m) / N.m or Joule [as because W=f.d]

• If Force =1 N and d=1m, then the work done bythe force wil be 1 J.

## Dimensions of Work

• Here we derived the dimensions of Work of the topic Work Power and Energy formulas, important for SSC and RRB NTPC, often simple MQ’s asked from tis particular point like what is the dimensions of work ?

• The dimensions of work is [ML2T–2].
Formula of Work is – Work (W) = Force (f) . Displacement (d)
• According to Newton’s second law of motion force equal to mass multiplied by acceleration. [ Force (F) = Mass (m). Acleration (a)]
• The Acceleration has the dimensions of velocity (L/T) divided by time (T), i.e. L T−2 and the dimension of mass is M.
• Therefore the dimensions of Force is MLT-2
• From the above we can easily derived the dimensions of Work that is MLT-2 . L or ML2T-2. (dimensions of Displacement is L)

• The unit and dimensions of both the work and energy is same, i.e Joule and ML2T-2 respectively.

• Alternative Units of Work/Energy in J
• Erg [1 erg = 10-7 J ]
• Electron Volt (eV) = [ 1 eV = 1.6 ✕ 10-19 J ]
• Calorie (cal) = [ 1 cal = 4.186 J ]
• Kilowatt Hour (kWh) = [1 kWh = 3.6✕ 106 J ]

## Different Types of Work Done | Negative | Positive

Both the points Types of Work done and condition for no work or zero work (next point)  from the chapter  Work Power and Energy formulas are  most important for making tricky questions.

Based on the angel (θ) between the direction of force and displacement the Work can be both positive and negative.

• Condition for Positive work

1. If θ is between 0o and 90o, cos θ is positive therefore, the work done is also positive.
• Example:- Suppose the angel (θ) between the direction of force and displacement is 0o. So, W =fdCos θ = fdCos θ = fd [Cos 0 =1]
2. In another words,when the force and displacement are in the same direction, then the work done will be positive.
• Example:-A boy puls an object towards himsef.

• Condition for Negative work

1. If θ is between 90o and 180o, cos θ is negative, therefore, the workd done is also negative.
• Example : In case of frictional force which opposes the displacement formd an ange between the direction of force and displacement is 180o, i.e θ = 180o. or W=fd Cos 180o = – fd [Cos 180 = -1]
• In this case the work done by friction is negative.
2. In another words,when the force and displacement are in the same direction, then the work done will be positive.
• Example:- A body is made to slide over a rough horizontal surface, then frictional force acts in the direction opposite to the direction of displacement. So work  done by friction will be negative.

## Condition of No work is done or Zero Work

• Condition 1. When the displacement is zero [d=0]
• Example 1: A weightlifter holding a 150 kg mass steadily on his shoulder for 30 s does no work on the load during this time.

• Example 2: When we push hard against a rigid brick wall, the force we exert on the wall does no work. Yet our muscles are alternatively contracting and relaxing and internal energy is being used up.

• Exampe 3: If a bodyis moving on circle, then after completing one circle work done is zero. because the displacementof the body  is zero.

• Condition 2: When the force is zero.
• Example: A block moving on a smooth horizontal table is not acted upon by a horizontal force (since there is no friction), but may undergo a large displacement.

• Condition 3: the force and displacement are mutually perpendicular.
• In that case the value of angel between the the direction of force and displacement is 90o. [ θ = π/2 rad = 90o]
• Work done W= fd cos (π/2) = 0 [Cos 90o = 0 ]
• Example 1: A block moving on a smooth horizontal table, the gravitational force mg does no work since it acts at right angles to the displacement.

• Exampe 2: If a coolie is moving forward carrying load on his head, in this case force is acting verticallly downward (weight of load) and displacement is along horizontal direction, so work done is Zero.

## Sampel MCQ’s on ‘Work’ from the chapter Work Power and Energy

Here we provide all the mcq’s on ‘Work’ of the topic Work Power and Energy formulas which is important for almost all  competitive exams like SSC, RRB NTPC, CDS, UPSC and all state PSC’s (both prelims  and mains)

1. Which of the following pairs of physical quantities have the same dimensions?
(SSC CHSL (10+2) LD 2015)
A. Force and Power
B. Work and Power
C. Work and Energy
D. Momentum and Power

2. If a body moves with a constant speed in a circle _
(SSC CHSL (10+2) DEO & LDC 2014)
A. no work is done on it
B. no force acts on it
C. no acceleration is produced in it
D. its velocity remains constant

3. One electron volt is equal to _
A. 6× 10-17 J
B. 6× 10-19 J
C. 1.6× 10-17 J
D. 6.5× 10-10 J

4. The SI unit of Work is _
A. Joule-second
B. Kwhr
C. Watt
D. Joule

5. The Work Done by the Centripetal Force for a Body Moving in a Circular Path is __?
A. Negative
B.Positive
C.Constant
D. Zero

6. The work done is Zero if _
A. The body shows displacement in the opposite direction of the force applied.
B. The body shows displacement in the same direction as that of the force applied.
C. The body shows a displacement in perpendicular direction to the force applied.
D. The body masses obliquely to the direction of the force applied

7. The unit of work is joule. The other physical quantity that has same unit is _
A. power
B. velocity
C. energy
D. force

8.  When can one say that work is done on the body _
A. When the body experiences force
B. When there is an increase in energy because of mechanical influence
C. When the body moves a certain distance
D. None of the above

9. When the force retards the motion of body, the work done is _
A. Positive
B. Negative
C. Zero
D. None of these

10. A man pushes a wall and fails to displace it, he does _
A. Maximum positive word
B. Negative work
C. Positive but not maximum work
D.  No work at all

11. The work done by a Boy who carrying a box on his head is waking on a level road _
A. Positive
B. Negative
C. Zero
D. None of these

12. A metal ball moves in a frictionless inclined table without slipping. The word done by the table surface on the ball is
A. Positive
B. Negative
C. Zero
D. None of these

13. What happens to the body on which work is done _
A.First it loses then it gain
B. No change in the energy
C. It gains energy
D. It loses energy

14. On an object the work done does not depend upon_
A. Initial velocity of an object
B. Displacement
C. Force applied
D. Angle between force and displacement

15. What is the dimensions of Work?
A. M L2 T-2
B. M L2 T-3
C. M L-1 T-1
D. M L-3 T-1

16. Work is a _
A. Vector Quantity
B. Tensor quantity
C. Scalar Quantity
D. None of these

17. 1 erg equal to _
A.3.6× 107 J
B.10-10 J
C. 10-7 J
D.none of these

18. Work done by frictional force is _
A. Positive
B. Negative
C. Zero
D. None of these

19. Work done by the gravitational force on a body moving on a smooth
horizontal surface _
A. Positive
B. Negative
C. Zero
D. None of these

20. 1 newton-metre (N⋅m) is equal to _
A. 10-7 erg
B.0.2389 Cal
C. 1 Joule
D.  All of the above

Source – NCERT Class 11 Physics

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