Concept explainers
(a)
Find the given equation is dimensionally homogenous or not.
(a)
Answer to Problem 13P
The given equation is dimensionally homogenous and it is proved.
Explanation of Solution
Given data:
The equation is,
Here,
Formula used:
The SI unit expression in terms of base units as follows,
Calculation:
Find the given equation is dimensionally homogenous or not.
Substitute the units N for F, kg for
Here,
Equation (2) becomes,
Substitute the unit
From equation (4), Left-hand side (LHS) is equal to Right-hand side (RHS). Thus, the given equation is dimensionally homogenous and it is proved.
Conclusion:
Hence, the given equation is dimensionally homogenous and it is proved.
(b)
Find the given equation is dimensionally homogenous or not.
(b)
Answer to Problem 13P
The given equation is not dimensionally homogenous and it is proved.
Explanation of Solution
Given data:
The equation is,
Here,
Formula used:
The SI unit expression in terms of base units as follows,
Calculation:
Find the given equation is dimensionally homogenous or not.
Substitute the units N for F, kg for
Here,
Equation (6) becomes,
Substitute the unit
From equation (8), Left-hand side (LHS) is not equal to Right-hand side (RHS). Thus, the given equation is not dimensionally homogenous and it is proved.
Conclusion:
Hence, the given equation is not dimensionally homogenous and it is proved.
(c)
Find the given equation is dimensionally homogenous or not.
(c)
Answer to Problem 13P
The given equation is not dimensionally homogenous and it is proved.
Explanation of Solution
Given data:
The equation is,
Here,
Formula used:
The SI unit expression in terms of base units as follows,
Calculation:
Find the given equation is dimensionally homogenous or not.
Substitute the units N for F, kg for
Here,
Equation (10) becomes,
Substitute the unit
From equation (12), Left-hand side (LHS) is not equal to Right-hand side (RHS). Thus, the given equation is not dimensionally homogenous and it is proved.
Conclusion:
Hence, the given equation is not dimensionally homogenous and it is proved.
(d)
Find the given equation is dimensionally homogenous or not.
(d)
Answer to Problem 13P
The given equation is dimensionally homogenous and it is proved.
Explanation of Solution
Given data:
The equation is,
Here,
Formula used:
The SI unit expression in terms of base units as follows,
Calculation:
Find the given equation is dimensionally homogenous or not.
Substitute the units N for F, kg for
Substitute the unit
From equation (15), Left-hand side (LHS) is equal to Right-hand side (RHS). Thus, the given equation is dimensionally homogenous and it is proved.
Conclusion:
Hence, the given equation is dimensionally homogenous and it is proved.
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Chapter 6 Solutions
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