Q#1
The dimensions ML⁻¹T⁻² may correspond to(a) work done by a force
(b) linear momentum
(c) pressure
(d) energy per unit volume.
Answer: (c), (d).
Work done and energy have the same unit and given as Force x distance = [MLT⁻²][L] = [ML²T⁻²]. Hence the option (a) is not correct.
Linear momentum = mass x velocity = [M][LT⁻¹] = [MLT⁻¹]. Hence the option (b) is not correct.
Pressure = Force/Area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²]. So, the option (c) is correct.
Energy per unit volume = Energy/volume = [ML²T⁻²]/L³ = [ML⁻¹T⁻²]. So, the option (d) is correct.
Q#2
Choose the correct statement(s):
(a) A dimensionally correct equation may be correct.
(b) A dimensionally correct equation may be incorrect.
(c) A dimensionally incorrect equation may be correct.
(d) A dimensionally incorrect equation may be incorrect.
Answer: (a), (b), (d).
A dimensionally correct equation may or may not be correct. Hence the option (a) and (b) are correct.
A correct equation must be dimensionally correct too. Hence a dimensionally incorrect equation will not be correct. Option (c) is wrong and the option (d) is true.
Q#3
Choose the correct statements:
(a) All quantities may be represented dimensionally in terms of the base quantities.
(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
(c) The dimension of a base quantity in other base quantities is always zero.
(d) The dimension of a derived quantity is never zero in any base quantity.
Answer: (a), (b), (c).
All other quantities are derived quantities. Hence they may be represented in terms of the base quantities. Option (a) is correct.
Each base quantity is independent of other base quantities. Hence none of the base quantities can be represented dimensionally in terms of other base quantities. Due to this, the dimension of a base quantity in other base quantities is always zero. Option (b) and (c) are correct.
The dimensions of a derived quantity may be zero in any base quantity. For example 'velocity' has zero dimension in mass [M]. The frequency has zero dimensions in mass [M] and length [L]. Hence the option (d) is incorrect.
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