The SI base unit for mass is __________.
A gram
B kilogram
C pound
D slug
Kilogram (kg) is SI base unit for mass.
The notation [L]^n means __________.
A unitless
B dimension of length raised to power n
C mass to power n
D time to power n
[L]^n denotes length dimension exponent n.
The “pole” in polar coordinates corresponds to __________.
A origin
B infinity
C axis
D unit circle
Pole is the origin in polar coordinates.
The integral of solid angle over a hemisphere equals __________.
A 2π sr
B 4π sr
C π sr
D 8π sr
Hemisphere solid angle = 2π sr.
Which symmetry implies conservation of center-of-mass momentum?
A Time reversal
B Translation in space
C Rotation
D Parity
Spatial translation symmetry leads to linear momentum conservation.
If a physical formula is dimensionally correct, then __________.
A it must be numerically correct
B it could still be wrong by dimensionless constants
C it is always experimentally verified
D it contains no units
Dimensional correctness necessary but not sufficient; dimensionless factors may be missing.
The product of a vector and a scalar results in a __________.
A vector
B scalar
C tensor
D matrix
Scaling a vector yields a vector.
Which of these is a measure of spread in repeated measurements?
A mean value
B standard deviation
C mode
D median
Standard deviation quantifies spread.
The derivative dθ/dt when θ is an angle gives __________.
A angular displacement
B angular velocity
C angular acceleration
D frequency
dθ/dt is angular velocity.
Which of the following is conserved in absence of external torques?
A Angular momentum
B Linear momentum only if no external forces
C Energy only if no non-conservative forces
D All of the above (under their respective conditions)
Specifically, angular momentum conserved if no external torque.
A physical quantity expressed as kg·m·s^-2 is __________.
A Joule
B Newton
C Pascal
D Watt
kg·m·s^-2 = N (force).
The error that can be reduced by calibration is __________.
A random error
B systematic error
C intrinsic quantum uncertainty
D Poisson error
Calibration can correct systematic errors.
Which coordinate is cyclic for rotation about z-axis?
A z
B φ (azimuthal angle)
C ρ
D r
φ parameterizes rotations about z-axis.
The divergence of a curl of any vector field is always __________.
A maximum
B zero
C one
D undefined
Identity: ∇·(∇×A) = 0.
Which of the following is a pseudoscalar example?
A Mass
B Scalar triple product (a·(b×c))
C Speed
D Temperature
Scalar triple product reverses sign under parity → pseudoscalar.
The SI unit of luminous intensity is __________.
A candela
B lumen
C lux
D watt
Candela (cd) is SI base for luminous intensity.
For two perpendicular axes in plane, the coordinate transformation between Cartesian and polar involves __________.
A hyperbolic functions
B trigonometric functions (sin, cos)
C logarithms
D exponentials
x = r cosθ, y = r sinθ use trig functions.
The Laplacian operator in Cartesian coordinates for scalar φ is ∇²φ = __________.
A ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²
B ∂φ/∂x + ∂φ/∂y + ∂φ/∂z
C ∇φ × ∇φ
D gradient squared
Laplacian equals sum of second partial derivatives.
The unit of surface density (mass per unit area) is __________.
A kg/m²
B kg/m³
C kg·m²
D m²/kg
Surface density units are mass/area.
When a system exhibits discrete rotational symmetry of 120°, which component of angular momentum is quantized accordingly in quantum contexts?
A Lx only
B Lz modulo 3 (in some symmetric potentials)
C None in classical context
D All components equally
Discrete rotational symmetry (C3) constrains angular momentum modulo symmetry; classical question simplified.
The magnitude of a vector v = 3i + 4j (in unit vectors) is __________.
A 5
B 7
C √7
D 1
|v| = √(3^2 + 4^2) = 5.
If measured values are 2.0, 2.1, 1.9, the mean is __________.
A 2.0
B 2.1
C 1.9
D 2.5
Mean = (2.0+2.1+1.9)/3 = 6.0/3 = 2.0.
The determinant of rotation matrix in 3D is __________.
A 0
B 1
C −1
D depends on angle
Proper rotation matrices have determinant +1.
The speed of light c has dimension __________.
A [L][T^-1]
B [M][L][T^-2]
C [L^2][T^-1]
D [T]
Speed dimension length/time.
A quantity that obeys superposition principle (linear) is called __________.
A linear
B non-linear
C chaotic
D random
Superposition applies to linear systems.
When you add two quantities with different dimensions you get __________.
A meaningful result
B dimensionally incorrect expression
C dimensionless number
D scalar
Adding different dimensions is invalid.
In measurement reporting significant figures, trailing zeros after decimal are __________.
A significant
B always not significant
C never used
D ambiguous
Trailing zeros after decimal indicate significance.
A point in spherical coordinates is described by (r, θ, φ). Here θ is usually __________.
A azimuthal angle measured in xy-plane
B polar (colatitude) angle from z-axis
C radial velocity
D temperature
Convention: θ often polar angle from z-axis, φ azimuthal.
The energy radiated uniformly by a point source is spread over area proportional to r^2 because of __________.
A conservation of energy and geometry of sphere surface
B energy creation
C friction
D medium absorption only
Power through spherical surface spreads over 4πr^2.
Which of the following transforms like a vector under rotations but changes sign under parity?
A True scalar
B Vector (polar vector)
C Pseudovector (axial vector)
D None
Polar vectors (like displacement) invert under parity; axial vectors (like angular momentum) do not.
If measured time is reported to 2 decimal places, the least count is __________ (in same units).
A 10^−2 of unit
B 10^2
C 1
D 10^−1
Two decimals → resolution 0.01 of unit.
The conservation law that is empirical and observed in many particle reactions is conservation of __________.
A baryon number
B time
C length
D velocity
Baryon number conserved in standard non-exotic processes.
The magnitude of solid angle subtended by a small circular area of radius a at distance r (a<
A True
B False
C Only for hemisphere
D Only for sphere
For small patch, dΩ ≈ area / r^2.
The Jacobian determinant appears when changing variables in integrals; for polar from Cartesian the Jacobian is __________.
A r
B 1/r
C r^2
D sinθ
dx dy = r dr dθ → Jacobian = r.
Which of these is a correct dimensionless combination?
A speed/c
B mass × length
C time × length
D momentum × charge
v/c is dimensionless ratio.
The dot product a·b equals |a||b|cosθ; dimensionally this means __________.
A units multiply and cosθ dimensionless
B units add
C units change sign
D always dimensionless
Dot product multiplies magnitudes (units multiply) and cosθ is pure number.
The Laplace equation ∇^2φ = 0 often appears in problems with __________.
A steady-state potentials (electrostatics, steady heat flow)
B oscillatory solutions only
C frictionless motion only
D quantum entanglement
Laplace’s equation arises in steady-state potential problems.
Which of the following is a conserved quantity in closed mechanical systems (no non-conservative forces)?
A Mechanical energy
B Angular momentum only if torque zero
C Linear momentum if net external force zero
D All of the above under stated conditions
Each conservation applies under specific absence of sources.
If f has the dimension of energy and g has dimension of length, then f/g has dimension __________.
A [M][L][T^-2]
B [L]
C [T]
D [M][L^0][T^-2]
Energy/length = force → M L T^-2.
The integral of dΩ over a cone full solid angle gives 2π(1 − cosα). This integrates to 2π when α = 90° — this is an example of __________.
A coordinate-specific identity
B solid-angle calculation
C vector addition
D unit conversion error
It’s a standard solid-angle formula.
The physical constant with units of J·s is __________.
A Planck’s constant (h)
B Boltzmann constant
C Gravitational constant
D Speed of light
Planck’s constant h has units J·s.
The accuracy of an instrument refers to __________.
A closeness to true value
B reproducibility
C number of decimal places only
D price of instrument
Accuracy measures closeness to true value.
In 2D, a rotation by 270° is equivalent to rotation by __________.
A −90°
B 90°
C 180°
D 360°
270° = −90° rotation.
Which of the following is not conserved in general relativity in the same simple form as in Newtonian physics?
A Energy (global)
B Local energy–momentum conservation still holds
C Angular momentum local conservation applies in symmetries
D Baryon number generally conserved
Global energy conservation is subtle in general curved spacetimes; local energy-momentum conservation holds.
The standard deviation of a set of identical repeated measurements that are purely random noise around true value reflects __________.
A measurement precision
B instrument bias
C zero reading
D nothing
Standard deviation quantifies precision/spread.
If the magnitude of vector sum of two equal vectors at 60° is asked, the result is 2v cos(30°) = __________ times v.
A √3
B 1
C 2
D 0
2v cos30° = 2v*(√3/2)=√3 v.
Which of these is required to check dimensional consistency of an equation?
A Make sure exponents of base dimensions match both sides
B Evaluate numerically
C Plug in numbers only
D None
Dimensional analysis requires matching exponents of base dimensions.
The radial unit vector in polar coordinates changes direction with position; its derivative with respect to θ equals __________.
A θ-hat (unit tangential vector)
B zero
C its negative
D radial vector squared
d(êr)/dθ = êθ (tangential unit vector).
The conservation statement “dQ/dt = 0” for some quantity Q means Q is __________.
A increasing
B decreasing
C conserved (constant in time)
D oscillating
Time derivative zero indicates constant.
If you measure current and time to get charge, the propagated fractional uncertainty in charge is __________ (if uncertainties are independent).
A sum of fractional uncertainties of current and time
B difference
C product
D zero
For product Q = I·t, fractional uncertainties add approximately.