Class notes Physics

Chapter 1
Short Questions and Numerical Problems

,All the dear students, please solve all these questions
your assignment copy ( Register) and practice similar
questions from the reference materials. If you have a
confusion or you find any mistakes in this material,
inform me as well. Thank you!

, 𝟐𝑻 𝐜𝐨𝐬 𝜽
1. Check the correctness of the relation h = , where the symbols
𝒓𝝆𝒈
have their usual meaning.
2𝑇 cos 𝜃
Solution: Given, h = ……………(i)
𝑟𝜌𝑔
Now, the dimension of LHS= dimension of ‘h’
= height
=m
= [L]
2𝑇 cos 𝜃
The dimension of RHS = dimension of
𝑟𝜌𝑔
𝑇
= ( here, 2 cos 𝜃 is dimensionless)
𝑟𝜌𝑔
[ML0T−2]
=
[L].[ML−3T0].[LT−2]
= [L]
Here, the dimension of LHS= dimension of RHS. So, the given relation is
dimensionally correct.

, 2. Find the dimensions of Planck’s constant ‘h’ from the given relat
𝒉
𝝀 = , where 𝝀 is wavelength and p is the momentum of photon.
𝒑
ℎ
Solution: Given relation is 𝜆 =
𝑝
Or, h = 𝜆.p
Here, 𝜆 is measured in meter (m) and p is in kgms-1.
Substituting the dimensions,
h = m. kgms-1
or, h = kgm2s-1
Or, h = [ML2T-1]
Hence, the dimensional formula of Planck’s constant is [ML2T-1]
and the dimensions are 1 in mass, 2 in length and -1 in time.