Chapter 1: Physical World, Measurement & Mathematical Tools (Set-2)

The SI unit of solid angle is dimensionless but commonly written as __________.

A degree
B steradian (sr)
C radian
D newton

A scalar changes sign under parity if it is a __________.

A true scalar
B pseudoscalar
C vector
D tensor

Which conservation law would be directly violated if the laws changed with time?

A Momentum
B Energy
C Angular momentum
D Mass

The operation that rotates an object by 180° about an axis is a subset of __________.

A translations
B rotations
C inversions
D gauge transformations

Which of the following is a derived unit?

A Ampere
B Mole
C Joule
D Kelvin

The quantity 1 steradian corresponds to an area on a sphere of radius r equal to __________.

A
B r
C
D r⁰

If a measurement shows consistent deviation from true value due to instrument, that is __________.

A random error
B systematic error
C statistical error
D unavoidable quantum noise

Which coordinate system is used for a long straight wire problem often?

A Cartesian
B Spherical
C Cylindrical
D Polar

The dimension of gravitational constant G is __________.

A [M⁻¹][L³][T⁻²]
B [M][L⁻³][T²]
C [M][L²][T⁻¹]
D [L][T⁻²]

A vector that does not change direction under coordinate rotation is called __________.

A scalar
B pseudovector
C tensor
D vector

The coordinate transformation x′ = x cosθ − y sinθ, y′ = x sinθ + y cosθ represents a __________.

A translation
B rotation by θ in 2D
C scaling
D reflection

If length L is measured as 12.0 ± 0.6 cm, percent uncertainty is __________.

A 0.5%
B 5%
C 50%
D 0.05%

The dot product of two perpendicular vectors is __________.

A maximum
B zero
C undefined
D negative

A function f has dimension [L][T⁻¹]; integrating f with respect to time gives quantity with dimension __________.

A [L][T⁻²]
B [L]
C [L][T⁰]
D [L][T⁰] (same as [L])

The smallest angle you can measure with a protractor is called its __________.

A least count
B uncertainty
C accuracy
D bias

A system invariant under rotation by any angle has continuous rotational symmetry, leading to conservation of __________.

A linear momentum
B energy
C angular momentum
D entropy

The total solid angle around a point is __________ steradians.

A
B
C π
D

The derivative d²x/dt² has dimension __________.

A [L][T⁻²]
B [L][T⁻¹]
C [M][L⁻²]
D [T]

When adding two vectors graphically, the rule used is the __________.

A parallelogram rule
B Pythagorean rule only
C scalar rule
D division rule

If a certain law holds in one inertial frame and all inertial frames, this property is called __________.

A frame-dependence
B Galilean invariance (or relativity principle)
C gauge symmetry
D none

The value of π sr in steradian measurement is dimensionless and equals approx __________.

A 3.14 sr
B 180 sr
C 1 sr
D 6.28 sr

The cross product of two parallel vectors is __________.

A maximum
B zero
C parallel to them
D undefined

Which of the following statements is correct about measurements?

A Accuracy refers to closeness to true value
B Precision refers to closeness of repeated measurements to each other
C Both A and B
D Neither

The dimensional formula of frequency is __________.

A [T⁻¹]
B [L][T⁻¹]
C [M][T⁻²]
D [I]

If a light source emits uniformly in all directions, the intensity per unit solid angle is measured in __________.

A watt per steradian
B watt per meter²
C watt per second
D watt per kilogram

Which of the following is invariant under time reversal (t→−t)?

A Velocity
B Acceleration
C Position
D Linear momentum sign depends on velocity so changes sign

The quantity [M^0 L^0 T^0] is __________.

A length
B mass
C dimensionless
D time

What operation on coordinates corresponds to mirror reflection in the yz-plane?

A x→−x, y→y, z→z
B x→x, y→−y, z→−z
C x→−x, y→−y, z→−z
D x→x, y→y, z→z

The unit of moment of inertia is __________.

A kg·m²
B kg/m²
C Nm
D m/s

For small errors, the relative error in quotient x/y approximately equals __________.

A (Δx − Δy)/ (x/y)
B Δx/x + Δy/y
C Δx/x + Δy/y (with Δy sign reverse if in denominator)
D Δx/x − Δy/y

The parity operation changes a right-handed coordinate system to __________.

A right-handed again
B left-handed
C same as before
D undefined

An object with mass m moving at constant velocity in free space will conserve __________.

A kinetic energy only
B linear momentum only
C both linear momentum and kinetic energy if no external forces
D neither

Which of the following is not a space–time symmetry?

A Translation in space
B Rotation in space
C Translation in time
D Chemical reaction

The area of a spherical cap on a sphere of radius r with polar angle α is 2π r^2 (1 − cosα). This formula relates to __________.

A chord length
B solid angle
C circumference
D density

In a lab, repeatedly measuring a quantity yields values clustered but all far from true value. This indicates __________.

A high accuracy, low precision
B low accuracy, high precision
C both high
D both low

Unit conversion from km/h to m/s uses factor __________.

A divide by 3.6
B multiply by 3.6
C multiply by 3600
D divide by 3600

Which of the following is a tensor of rank 2?

A Scalar
B Vector
C Stress tensor
D Number

The physical quantity conserved when a system is invariant under rotation about z-axis is the __________.

A z-component of angular momentum
B x-component of angular momentum
C total mass
D energy

The vector triple product a×(b×c) equals __________.

A (a·c) b − (a·b) c
B (a·b) c − (a·c) b
C zero always
D (b·c) a

The best measure of central tendency for skewed data is __________.

A mean
B median
C mode
D range

Which symmetry combined with charge conjugation and time reversal is often considered (CPT)?

A P only
B C, P, and T together (CPT theorem)
C None
D Gauge

In a unit conversion, 1 inch = 2.54 cm exactly because __________.

A arbitrary choice
B defined by international agreement
C derived from fundamental constants
D varies with temperature

Which of the following is conserved in a closed chemical system ignoring nuclear reactions?

A Mass (baryon number)
B Energy only
C Neither mass nor energy
D Charge only

The gradient operator ∇ acting on a scalar field gives a __________.

A scalar
B vector
C tensor
D matrix

An angle measured in steradians is associated with __________.

A planar angle
B solid angle
C linear distance
D volume

If two physical quantities are multiplied, their dimensions __________.

A add (exponents add)
B subtract
C multiply numerically only
D cancel always

Which of the following operations does not change the magnitude of a vector but can change its direction?

A Scaling by factor >1
B Rotation
C Reflection with inversion of magnitude
D Multiplication by zero

The SI base for temperature is __________.

A Celsius
B Fahrenheit
C Kelvin
D Rankine

The dimension of kinetic energy (1/2 mv^2) is __________.

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

In measuring angles, conversion from degrees to radians uses factor π rad = __________ degrees.

A 90°
B 360°
C 180°
D 60°