30 Questions
What is the dimensional formula of angular momentum in terms of v, A, and F?
Fv³A⁻²
What is the correct relation between the largest mass (m) that can be moved by a flowing river and the velocity (v), density (ρ) of river water, and acceleration due to gravity (g)?
m ∝ ρv⁶g³
What is the unit of acceleration due to gravity (g) in the given problem?
[LT⁻²]
What is the unit of velocity (v) in the given problem?
[LT⁻¹]
Which of the following is not a fundamental quantity in the given problem?
angular momentum
What is the terminal velocity of a small steel ball in a viscous liquid?
The constant velocity of the ball after some time
What determines the terminal velocity of a small steel ball in a viscous liquid?
The mass of the ball, coefficient of viscosity, radius, and acceleration due to gravity
Which of the following has the dimension [ML⁻¹T⁻¹]?
Coefficient of viscosity
What is the correct relation between terminal velocity and other physical quantities?
vT ∝ mg/ηr
What is the purpose of dimensional analysis in the given problem?
To check the accuracy of the given formula
If F2 = 1 in two systems of relations among velocity, acceleration, and force, then what can be inferred about the relation between F and v?
F α 2v1
If M2 = α^3 M1 and L2 = α^2 L1, then what can be inferred about the relation between T2 and T1?
T2 = α^2 T1
If a2 = αβ a1, then what can be inferred about the relation between v2 and v1?
v2 = αβ v1
What is the relation between L2 and L1 in the given system?
L2 = α^2 L1
What is the dimension of the coefficient of rigidity in the given problem?
[ML⁻¹T⁻¹]
What is the correct dimension of the time period of the oscillating block?
[T]
What is the dimension of the force applied to the block A?
[MLT⁻²]
If the mass of the block A is increased by a factor of 2, what will be the effect on the time period of the oscillations?
The time period will increase by a factor of 2.
What is the relation between the dimension of the length and the dimension of the time period?
The dimension of the length is square root of the dimension of the time period.
What is the correct expression for the time period of the oscillating block?
T = 2π √(ML/η)
If the coefficient of rigidity is increased by a factor of 2, what will be the effect on the time period of the oscillations?
The time period will decrease by a factor of 2.
What is the dimension of the product ML in the given problem?
[ML⁺¹]
What is the correct relation between the dimension of the mass and the dimension of the coefficient of rigidity?
[M] = [η][L]⁻¹
What is the purpose of dimensional analysis in the given problem?
To check the accuracy of the given formulae.
What is the primary purpose of significant figures in physics?
To indicate the precision of a measurement
A physical quantity has a dimension of [ML^(-1)T^(-1)]. What can be said about the quantity?
It is a derived quantity
What is the maximum number of physical quantities that can be used to derive a formula using dimensional analysis?
3
What is the primary limitation of dimensional analysis?
It cannot be used to derive formulas involving more than 3 physical quantities
What can be said about a formula that cannot be derived using dimensional analysis?
Its dimensional correctness can be checked using dimensional analysis
What is the significance of a large number of significant figures in a measurement?
It indicates a high degree of precision in the measurement
Determine the dimensionally correct relation for the terminal velocity of a small steel ball falling under gravity through a viscous liquid. This quiz is based on a problem from CPMT, CBSE, and NCERT exams.
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