One of the first things you learn in physics class is the law of universal gravitation.
(a)
S.I. unit of
Answer to Problem 74P
S.I. unit of
Explanation of Solution
Expression for gravitational force,
Here, the gravitational constant is
Dimensional formula for
Here, dimension of mass is
Dimensional formula for mass,
Dimensional formula for
Calculation:
Rearrange the Equation (I) for
Substitute
Conclusion:
Therefore, the S.I unit of
(b)
The non dimensional expression for
Answer to Problem 74P
The required expression is
Explanation of Solution
Write the expression for number of
Here, the number of variables are
Substitute
Therefore, the number of
Write the expression for first
Write the expression for the second
Calculation:
The dimensional formula for
Substitute
Compare the exponential coefficient of
Compare the exponential coefficient of
Compare the exponential coefficient of
Substitute
Substitute
Compare the exponential coefficient of
Compare the exponential coefficient of
Compare the exponential coefficient of
Substitute
From Equation (VII) and Equation (IX).
Here, the constant is
Substitute
Conclusion:
The required expression is
(c)
The functional relation between
Answer to Problem 74P
Any functional relation is possible between the two pi terms.
Explanation of Solution
Write the expression for the first pi term.
Write the expression for the second pi term.
Calculation:
Substitute
Substitute
Conclusion:
Any functional relation is possible between the two pi terms.
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Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
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