Modern Physics and Mechanics. PHY 1501

Chapter 2
Units and Measurement

1.Name the fundamental(base) quantities and units according to SI system.




2.Define angle




3.Define solid angle




4.Write the dimensional formulae of following derived quantities.
Area -L2 Work or energy - ML2T−2
Volume -L3 Power - ML2T−3
Density -ML−3 Pressure - ML−1T−2
Velocity- LT−1 Stress - ML−1T−2
Acceleration - LT−2 Modulus of elasticity- ML−1T−2
Momentum - MLT−1
Force - MLT−2

5.Write two physical quantities having no unit and dimension
Relative density, strain
…………………………………………………………………………………………………………………………………..
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, Seema Elizabeth, MARM Govt HSS Santhipuram, Thrissur


6.Write two physical quantities that have unit but no dimension
Plane angle, solid angle, angular displacement 7.




8.




9.Name and state the principle used to check the correctness of an equation.
Principle of homogeneity of dimensions.
For an equation to be correct the dimensions of each terms on both sides of the
equation must be the same
Or
The magnitudes of physical quantities may be added or subtracted only if they
have the same dimensions

10. Using the method of dimension check whether the equation is dimensionally
correct or not




Since the dimensions of all terms are not same the equation is not correct


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,11. Using the method of dimension check whether the equation is dimensionally
correct or not




Since the dimensions of all terms on both sides are same the equation is dimensionally
correct correct

12. Using the method of dimension check whether the equation is dimensionally
correct or not




13.Check the dimensional correctness of the equation E=m𝐜𝟐




14.In the given equation v = x + at , find the dimensions of x.
(where v= velocity , a=acceleration , t=time)




15. In the given equatio x= a + bt + c𝐭𝟐 , find the dimensions of a,b and c.
(where x is in meters and t in seconds)




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16.The Van der waals equation of 'n' moles of a real gas is (P+𝑽𝟐)(V−b)=nRT. Where P is
the pressure, V is the volume, T is absolute temperature, R is molar gas constant and a, b,
c are Van der waal constants. Find the dimensional formula for a and b.
𝐚
(P+𝐕𝟐)(V−b)=nRT.
By principle of homegeneity, the quantities with same dimensions can be added or subtracted.
a
[P] =[V2]
[a] =[PV2]
=ML−1T−2 x L6
[a] = ML5T−2

[b] = [V]
[b] =L3
17.Derive the equation for kinetic energy E of a body of mass m moving
with velocity v




18.Suppose that the period of oscillations of a simple pendulum depends on its mass of
the bob(m),length(l) and acceleration due to gravity(g).Derive the expression for its
time period using the method of dimensions.




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