Physics ( Std. XI ) - Theory
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| Ch. No. | Name of Chapter | No. of Pages |
| 01 | Physical World | |
| 02 | Measurement and System of Units | |
| 03 | Motion in One and Two Dimensions | |
| 04 | Laws of Motion | |
| 05 | Work, Energy and Power | 12 |
| 06 | Dynamics of a System of Particles | 3 |
| 07 | Rotational Motion | 15 |
| 08 | Gravitation | 6 |
| 09 | Mechanics of Solids | |
| 10 | Fluid Mechanics | 18 |
| 11 | Kinetic Theory of Gases | 9 |
| 12 | Thermodynamics | 14 |
| 13 | Transfer of Heat | |
| 14 | Oscillations | 10 |
| 15 | Waves |
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Chapter-05
( WORK, ENERGY AND POWER )
5.1 Work
“The product of force and displacement ( in the direction of force ), during
which the force is acting, is defined as work.”
When 1 N force is applied on a particle and the resulting displacement of the particle, in the
direction of the force, is 1 m, the work done is defined as 1 J ( joule ). The dimensional
formula of work is M1 L2 T -2.
direction of the applied force in all
cases. In the figure shown, the
displacement, d, makes an angle
θ with the applied force, F. According
to the definition of force,
Work, W = force × displacement in
the direction of the
force
= F ( d cos θ ) = ( F cos θ ) ( d )
= ( the component of force in the direction of displacement ) × ( displacement )
( i ) For θ = π / 2, work W = 0, even if F and d are both non-zero. In uniform circular
motion, the centripetal force acting on a particle is perpendicular to its displacement.
Hence, the work done due to centripetal force during such a motion is zero.
( ii ) If θ < π / 2, work done is positive and is said to be done on the object by the force.
( iii ) If π / 2 < θ < π, work done is negative and is said to be done by the object against the
force.
5.2 Scalar product of two vectors
Similarly, N is the foot of perpendicular from the head of
→ →
B to A and ON ( = B cos θ ) is the
magnitude of projection of
→ →
B on A .
∴ → → A ⋅ B = AB cos θ = B ( A cos θ ) = ( B ) ( OM )
= ( magnitude of
→B
) ( magnitude of projection of
→ →
A on B )
or
→ → A ⋅ B = AB cos θ = A ( B cos θ ) = ( A ) ( ON )
= ( magnitude of
→A
) ( magnitude of projection of
→ →
B on A )
Thus, scalar product of two vectors is equal to the product of magnitude of one vector with
the magnitude of projection of second vector on the direction of the first vector.
The scalar product of vectors is zero if the angle between the vectors θ = π / 2, positive if
0 ≤ θ < π / 2 and negative if π / 2 < θ ≤ π .
5.2 Scalar product of two vectors
The scalar product of two vectors,
→ →
A and B , also known as the dot product, is written by
putting a dot ( ⋅ ) between the two vectors and is defined as:
→ →
A ⋅ B = l
A ⋅ B = l
→
A
A
l l
→
→
B l cos θ = A B cos θ, where θ is the angle between the two vectors.
To obtain the scalar product of
→ →
A and B , they are to be drawn from
a common point, O, with the same
magnitudes and directions as shown in
the figure.
M is the foot of perpendicular from the
head of
→ →
A to B . OM ( = A cos θ ) is
the magnitude of projection of
→ →
A on B .
Similarly, N is the foot of perpendicular from the head of
→ →
B to A and ON ( = B cos θ ) is the
magnitude of projection of
→ →
B on A .
∴ → → A ⋅ B = AB cos θ = B ( A cos θ ) = ( B ) ( OM )
= ( magnitude of
→B
) ( magnitude of projection of
→ →
A on B )
or
→ → A ⋅ B = AB cos θ = A ( B cos θ ) = ( A ) ( ON )
= ( magnitude of
→A
) ( magnitude of projection of
→ →
B on A )
Thus, scalar product of two vectors is equal to the product of magnitude of one vector with
the magnitude of projection of second vector on the direction of the first vector.
The scalar product of vectors is zero if the angle between the vectors θ = π / 2, positive if
0 ≤ θ < π / 2 and negative if π / 2 < θ ≤ π .
