Torque is defined as:
A r×p
B r×F
C F×t
D p×v
Torque is the cross product of position vector and force.
SI unit of torque is:
A N
B J
C N·m
D J/s
Since torque = force × perpendicular distance.
Angular momentum of a particle is given by:
A Iα
B rF
C r×p
D mv²
Angular momentum is cross product of r and linear momentum.
Angular momentum is conserved when:
A No external force acts
B No external torque acts
C No internal force acts
D Velocity is constant
External torque affects angular momentum.
If torque is zero, angular momentum:
A Increases
B Decreases
C Remains constant
D Becomes zero
Zero torque means no change in angular momentum.
Direction of torque is given by:
A Right-hand rule
B Left-hand rule
C Newton’s rule
D Rutherford’s rule
Cross product uses right-hand rule.
A door is easiest to open when force is applied:
A Near hinges
B At midpoint
C At the edge
D Vertically downward
Torque increases with perpendicular distance.
Torque becomes zero when:
A Force increases
B Angle is 90°
C Displacement is zero
D Force is along the line of pivot
Torque = rFsinθ; sin0° = 0.
Rotational analogue of force is:
A Momentum
B Work
C Torque
D Angular momentum
Torque produces rotational acceleration.
Angular impulse equals change in:
A Linear momentum
B Angular momentum
C Torque
D Angular velocity only
Angular impulse = ΔL.
Moment of inertia depends on:
A Force only
B Mass distribution
C Speed
D Time
MoI depends on how mass is spread from axis.
SI unit of moment of inertia is:
A kg
B kg·m
C kg·m²
D N·m
MoI = mass × distance².
Which has greatest moment of inertia about central axis?
A Solid sphere
B Solid cylinder
C Hollow sphere
D Ring
Ring has all mass farthest from axis.
Moment of inertia of a rod about its centre is proportional to:
A L
B L²
C L³
D 1/L
I = 1/12 ML².
Doubling the distance of mass from axis increases MoI by:
A 2×
B 4×
C 8×
D 16×
I ∝ r².
Rotational inertia is greatest when:
A Mass is close to axis
B Mass is far from axis
C Body is rotating slowly
D Body is weightless
More distance → higher inertia.
Parallel axis theorem adds:
A ML
B ML²
C MH
D Md²
I = Icm + Md².
The rotational kinetic energy is:
A ½ m v²
B ½ I ω²
C Iα
D Iω
Rotational analogue of KE.
Moment of inertia of point mass is:
A mr
B mr²
C r²
D m/r
Definition: I = mr².
Least moment of inertia is for:
A Ring
B Hollow sphere
C Solid cylinder
D Solid sphere
Most mass near axis.
Rotational analogue of Newton’s second law:
A F = ma
B τ = Iα
C a = F/m
D p = mv
Torque = MoI × angular acceleration.
Angular acceleration is produced by:
A Linear force
B Centripetal force
C Torque
D Mass
Torque causes rotation.
Rolling without slipping means:
A v = rω
B v = ω/r
C v = r/ω
D v = r²ω
Condition for pure rolling motion.
If torque increases, angular acceleration:
A Increases
B Decreases
C Remains constant
D Becomes zero
Directly proportional.
Work done in rotational motion =
A τα
B τω
C τθ
D Iω
W = τθ.
Power in rotational motion is:
A Fv
B τω
C Iα
D dI/dt
Rotational power equivalent.
In pure rolling, friction:
A Does work
B Does no work
C Always increases KE
D Is zero
Point of contact has zero velocity → no work.
Angular velocity is measured in:
A rad/s
B rad
C m/s²
D m/s
Rate of change of angle w.r.t. time.
A body with larger MoI will:
A Rotate faster
B Resist rotational change more
C Fall freely
D Have more KE
Inertia resists change in motion.
Rotational equilibrium occurs when:
A Net torque = 0
B Net force = 0
C Angular momentum = 0
D MoI = 0
No net torque → no angular acceleration.
A central force:
A Depends on time
B Acts along line joining two bodies
C Acts perpendicular to radius
D Is always repulsive
Central force direction = radial.
Central forces always conserve:
A Linear momentum
B Torque
C Angular momentum
D Force
Torque = 0 about centre.
Non-central force causes:
A No torque
B Change in angular momentum
C No work
D No rotation
Non-central → off-centre → produces torque.
Gravitational force is a:
A Central force
B Non-central force
C Tangential force
D Perpendicular force
Acts along centre-to-centre line.
Central forces result in motion:
A Circular
B Parabolic
C Planar
D Random
Motion under central forces always lies in a plane.
Non-central forces change:
A Radius only
B Plane of motion
C Angular momentum
D Potential energy only
They exert torque.
Gravitational force follows:
A Linear law
B Inverse law
C Square law
D Inverse square law
F ∝ 1/r².
If distance becomes double, gravitational force becomes:
A Double
B Half
C One-fourth
D One-eighth
F ∝ 1/r².
Universal gravitational constant G depends on:
A Mass
B Radius
C Temperature
D Nothing
G is universal constant.
SI unit of G is:
A N
B N·m²/kg²
C Nm/kg
D kg/m²
Derived from Newton’s law of gravitation.
Weight of body is highest at:
A Equator
B Poles
C Centre of Earth
D Tropic of Cancer
g is maximum at poles.
Value of g decreases with:
A Depth below Earth
B Height above Earth
C Both depth & height
D Only rotation
g decreases above & below Earth’s surface.
Escape velocity from Earth depends on:
A Mass of body
B Shape of body
C Mass & radius of Earth
D Temperature
ve = √(2GM/R).
Orbital velocity is:
A √(GM/R)
B √(2GM/R)
C GM/R²
D GM/R
For circular orbit.
Value of acceleration due to gravity at Earth’s centre is:
A g
B 2g
C g/2
D 0
Symmetry → net force = 0.
Gravitational potential energy is:
A Always positive
B Always zero
C Always negative
D Always equal to KE
Zero at infinity; negative near Earth.
Satellite in circular orbit has:
A Zero KE
B Zero PE
C Constant total energy
D Variable acceleration
Energy remains constant in stable orbit.
Binding energy of satellite is:
A Positive
B Zero
C Negative
D Infinite
Bound systems have negative energy.
For planets, period of revolution obeys:
A Newton’s 1st law
B Kepler’s 3rd law
C Inverse cube law
D Coulomb’s law
T² ∝ r³.
Gravitational force between two bodies becomes zero when:
A Distance = 0
B Distance = ∞
C Mass = 0
D Both mass and distance large
At infinite separation, force → 0.