Q.1
What could be a correct expression for the speed of the ocean waves in term of its wavelength λ, the depth h of the ocean, the density ρ of sea-water, and the acceleration of free fall g?
A √(gλ)
Answer:
Only the base units of A √(gλ)
= √[(m s-2)(m)] = m s‑1
Is equivalent to the units of speed
Q.2
The relationship four physical quantites is given by the equation P = Q – RS.
Given that the equation is homogeneous, which of the following statements must be correct?
A P, Q, R and S all have the same units.
B P, Q, R and S are all scalar quantities.
C The product RS has the same units as P and Q.
D The product RS is numerically equal to (Q – P).
Answer: C
For the equiation to be homogeneous, P, Q and RS must have the same units.
Q.3
When a steel sphere of radius r falls at speed v though a liquid, it experiences a drag force F given by
F = arv,
where a is a constant. Which one of the following is a suitable SI unit for a?
A N B N s-1 C N m2 s-1
Answer: D
F = arv
Units of a = (units of F)/[(units of r)(units of v)]
= N/(m x m s-1) = N m-2 s
Q.4
The energy E of a photon of electromagnetic radiation of frekuency f is given by the expression
E = hf.
What are the SI base units of the Planck constant h?
A kg m s-1 B
Answer: B
h = E/f
base units of h = (base units of E)/(units of f)
= kg m2 s-2/s-1 = kg m2 s-1
Q.5
In term of kilogram (kg), metre (m), second (s) and ampere (A),
What are the base units of potential difference (the volt)?
A m and A only B s and A only C m, s and A only D kg, m, s and A
Answer: D
P.d = work done/charge
Base units of volt = base units of work/base units of charge
= (kg m2 s-2)/(As)
= kg m2 A-1 s-3
Q.6
If an object of mass m has momentum p,
which of the following quantities has identical base units to the expression p2/m?
A energy B force
Answer:
Base units of p2/m
= (kg m s-1)2/(kg)
= kg m2 s-2 ≡ base units of energy
Q.7
Which one of the following expressions has a base unit that is not the second (s)?
A 1/frequency
C √(length : acceleration)
Answer: D
Base units of mass : spring constant
= kg : (kg s-2) = s2 ≠ s
Q.8
Which quantity has a unit with an alternative form in term of just two different SI base units?
A area B charge
Answer: B
Among the gives options, only charge could be expressed in term of 2 different SI base units:
Q = It (in the usual notations)
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