SIR SADIQ’S NOTES
CHAPTER NO. 5
PHYSICS X
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SIR SADIQ’S NOTES
Q: Define scalar quantities.
SCALAR QUANTITIES
Physical quantities which can completely be specified by a
number (magnitude) having an appropriate unit are known as
"SCALAR QUANTITIES".
Scalar quantities do not need direction for their description.
Scalar quantities are comparable only when they have the
same physical dimensions.
Two or more than two scalar quantities measured in the
same system of units are equal if they have the same
magnitude and sign.
Scalar quantities are denoted by letters in ordinary type.
Scalar quantities are added, subtracted, multiplied or
divided by the simple rules of algebra.
EXAMPLES
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Work
Energy
electric flux
Volume
refractive index
Time
Speed
electric potential
potential difference
viscosity
density
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power
mass
distance
temperature
electric charge
electric flux
etc.
Q: define vector quantities.
Ans:
VECTORS QUANTITIES
Physical quantities having both magnitude and direction
with appropriate unit are known as "VECTOR QUANTITIES".
We can't specify a vector quantity without mention of
direction.
vector quantities are expressed by using bold letters with
arrow sign such as:
vector quantities cannot be added, subtracted, multiplied
or divided by the simple rules of algebra.
vector quantities added, subtracted, multiplied or divided
by the rules of trigonometry and geometry. Academy
EXAMPLES
• Velocity
• electric field intensity
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acceleration
force
momentum
torque
displacement
electric current
weight
angular momentum
etc.
REPRESENTATION OF VECTORS
On paper vector quantities are represented by a straight line
with arrow head
pointing the direction of vector or terminal
point of vector.
A vector quantity is first transformed into a suitable scale and
then a line is drawn with the help of the scale chosen in the
given direction
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Q: Explain addition if vectors by head to tail rule .
Ans :
HEAD TO TAIL RULE
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Suppose 2 vectors A and B having some magnitude and in
arbitrary (irragular) direction. To add these vectors the head of 1st
vector will be added with the tail of 2nd vector and so on
A
B
B
A
The vector which is drawn in such a way that the head is on the
head and the tail is on the tail is called resultant of a vector
R=A+B
A
B
The direction of the resultant vector is directed from the tail of
vector to the head of vector.
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Q: define resolution of vector. derive the formula for
rectangular components, magnitude of resultant and
direction of a vector.
Ans:
RESOLUTION OF A VECTOR
The splitting of a vector into its constituent rectangular
components is known as resolution of a vector.
Derivation
Suppose a vector A having some angle θ from the horizon and
which is making a vertical component Ay and a horizontal
component Ax respectively.
Where according to diagram
XYZ is formed (right angle
Y
)
Z
A
Ay
θ
-X
O
X
-Y
Ax
FOR MAGNITUDE OF COMPONENTS
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Using trigonometric ratios:
𝑠𝑖𝑛𝜃 =
𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑒𝑜𝑢𝑠
𝑠𝑖𝑛𝜃 =
𝑌𝑍
𝑋𝑍
𝑠𝑖𝑛𝜃 =
𝐴𝑦
𝐴
𝐴𝑦 = 𝐴 𝑠𝑖𝑛𝜃
Similarly
𝑐𝑜𝑠𝜃 =
𝑏𝑎𝑠𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑒𝑜𝑢𝑠
𝑐𝑜𝑠𝜃 =
𝑥𝑦
𝑋𝑍
𝑐𝑜𝑠𝜃 =
𝐴𝑥
𝐴
𝐴𝑥 = 𝐴 𝑐𝑜𝑠𝜃
FOR MAGNITUDE OF RESULTANT
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Since. a right
is formed
Therefore, using Pythagoras theorem.
𝐻2 = 𝐵2 + 𝑃2
(𝑋𝑍)2 = (𝑋𝑌)2 + (𝑌𝑍)2
𝐴2 = 𝐴𝑥 2 + 𝐴𝑦 2
Square root both sides
√𝐴2 = √𝐴𝑥 2 + 𝐴𝑦 2
𝑨 = √𝐴𝑥 2 + 𝐴𝑦 2
Where A is the magnitude of resultant
FOR MAGNITUDE OF DIRECTION
WE KNOW:
tan 𝜃 =
𝑝𝑒𝑟𝑝
𝑏𝑎𝑠𝑒
tan 𝜃 =
𝑌𝑍
𝑋𝑌
tan 𝜃 =
𝐴𝑦
𝐴𝑥
𝜃 = tan−1
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𝐴𝑦
𝐴𝑥
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