Chapter 1: Physical World, Measurement & Mathematical Tools (Set-1)

The study of Physics mainly concerns the __________.

A properties of languages
B behavior of living organisms
C nature and properties of matter and energy
D origin of species

Which of the following is not a primary goal of physics?

A Describe natural phenomena
B Predict future behavior of systems
C Create new languages
D Discover fundamental laws

Which quantity has both magnitude and direction?

A Temperature
B Force
C Mass
D Time

The SI base unit of length is the __________.

A meter
B liter
C foot
D yard

Dimension of velocity is __________.

A [M][L][T^-2]
B [L][T^-1]
C [M][L^2][T^-2]
D [T]

If a physical relation is dimensionally inconsistent, it is __________.

A always correct
B potentially wrong
C definitely correct
D dimensionless

The process of comparing a measurement to a standard is called __________.

A guessing
B measurement
C calibration
D modeling

A systematic error is best described as __________.

A random fluctuation
B bias that shifts all measurements
C due to human guessing
D caused only by rounding

The uncertainty that varies unpredictably from one measurement to another is called __________.

A systematic error
B random error
C calibration error
D absolute error

Which of the following reduces random errors the most?

A Use single measurement only
B Repeat measurements and average
C Change the measuring instrument brand frequently
D Ignore outliers always

A coordinate system that uses (r, θ) to locate a point is called __________.

A Cartesian
B Spherical
C Polar (plane)
D Linear

In 3D Cartesian coordinates, the point (0,0,0) is called the __________.

A origin
B pole
C focus
D node

Conversion from Cartesian (x,y) to polar (r,θ): r equals __________.

A x + y
B √(x^2 + y^2)
C x^2 + y^2
D x/y

The solid angle has SI unit __________.

A steradian
B radian
C degree
D meter

A full sphere subtends how many steradians?

A 2π sr
B 4π sr
C π sr
D 8π sr

The small solid angle dΩ on a sphere of radius r corresponding to area dA is given by __________.

A dΩ = dA / r
B dΩ = dA / r^2
C dΩ = r^2 dA
D dΩ = r dA

Space–time symmetry that reverses time coordinate t → −t is called __________.

A parity (P)
B time reversal (T)
C charge conjugation (C)
D rotation

Under parity (P) transformation, spatial coordinates (x,y,z) transform to __________.

A (x,y,z)
B (−x,−y,−z)
C (y,x,z)
D (1/x,1/y,1/z)

Conservation of linear momentum follows from which symmetry?

A Translational symmetry in space
B Time-translational symmetry
C Rotational symmetry
D Reflection symmetry

Energy conservation is associated with __________.

A spatial translation symmetry
B time translation symmetry
C rotation symmetry
D mirror symmetry

Which of the following is a conserved scalar in an isolated system?

A Total linear momentum
B Energy
C Both A and B
D Neither

Dimensions of torque (moment of force) are same as __________.

A energy
B pressure
C power
D velocity

The least count of a measuring instrument is __________.

A the largest value it can measure
B the smallest division it can resolve
C its mass
D its price

If measurement is reported as 2.30 ± 0.05 m, 0.05 is the __________.

A absolute error
B relative error
C percent error
D resolution

The relative error is defined as __________.

A absolute error × true value
B absolute error / measured value
C absolute error / true value
D measured value / absolute error

Which coordinate system is most convenient for problems with spherical symmetry?

A Cartesian
B Cylindrical
C Spherical
D Polar (2D)

The angle subtended by an arc of length s on a circle of radius r is θ = s/r in __________.

A degrees
B radians
C steradians
D revolutions

A steradian is analogous to a __________ in 2D.

A degree
B radian
C meter
D mole

If a physical law is invariant under rotation, then __________ is conserved.

A linear momentum
B electric charge
C angular momentum
D mass

Units of solid angle are dimensionless because:

A steradian equals m^2/m^2 so no dimension left
B steradian equals m/m^2
C it is measured in degrees
D it is fictitious

Which of the following is not an SI base quantity?

A Time
B Electric current
C Temperature
D Pressure

The dimension of electric charge in terms of [M],[L],[T],[I] is __________.

A [I][T]
B [M][L^2][T^-2]
C [Q] (no relation)
D [I]

If f(x) has dimensions of length and x is dimensionless, then df/dx has dimensions of __________.

A length
B 1/length
C dimensionless
D length^2

Which of the following is an example of a vector quantity?

A Electric potential
B Speed
C Displacement
D Temperature difference

A measurement reads 5.00 s with least count 0.01 s. An appropriate way to quote it with uncertainty is __________.

A 5.00 ± 0.01 s
B 5 ± 1 s
C 5.00 ± 0.5 s
D 5.000 ± 0.001 s

Which of the following changes sign under parity transformation?

A Scalar like mass
B Pseudoscalar like scalar triple product
C Energy
D Time

The conservation law stating that charge cannot be created or destroyed is called __________.

A conservation of mass
B conservation of electric charge
C conservation of momentum
D conservation of time

Which symmetry operation turns a particle into its antiparticle (in many contexts)?

A Parity (P)
B Charge conjugation (C)
C Time reversal (T)
D Translation

The dimensional formula of pressure is __________.

A [M][L^-1][T^-2]
B [M][L^2][T^-2]
C [M][L^-3]
D [L][T^-1]

If two measurements are 10.0 ± 0.2 and 3.0 ± 0.1, the percentage error of the first is __________ (approx).

A 2%
B 0.02%
C 20%
D 0.2%

Which statement about derived units is true?

A Derived units are unrelated to base units
B Derived units come from algebraic combinations of base units
C Derived units must be base units too
D Derived units cannot be expressed dimensionally

In cylindrical coordinates (ρ, φ, z), φ corresponds to __________.

A radial distance in xy-plane
B angle in xy-plane
C height along z
D temperature

Which of the following is conserved in an elastic collision between two particles in an isolated system?

A Kinetic energy and linear momentum
B Only kinetic energy
C Only momentum of one particle
D Neither energy nor momentum

A physical law invariant under time translation suggests:

A Momentum is conserved
B Energy is conserved
C Charge is conserved
D Volume is conserved

Solid angle subtended by a cone of half-angle α is 2π(1 − cosα). For α = 90°, solid angle equals __________.

A π sr
B 2π sr
C 4π sr
D 0 sr

A transformation (x→x+a) is an example of __________.

A rotation
B space translation
C parity
D scaling

Which of these is dimensionless?

A Reynolds number
B Force
C Energy
D Mass

The slope of a graph of displacement vs. time gives __________.

A acceleration
B velocity
C force
D energy

The physical quantity with dimension [L^3] is __________.

A volume
B pressure
C acceleration
D density

If the fractional uncertainties of two measured quantities x and y are 2% and 3%, the fractional uncertainty in product xy (approx) is __________.

A 1%
B 5%
C 6%
D 0%