Chapter 2: Kinematics, Laws of Motion & Non-Inertial Frames (Set-2)
Newton’s first law (law of inertia) states that a body remains at rest or moves with constant velocity unless acted on by a(n):
A magnetic field
B external net force
C internal force only
D change in temperature
Newton I: no net external force ⇒ no change in motion.
Newton’s second law in its standard form is:
A F = p t
B F = ma
C F = m/v
D F = mv²
Net force equals mass times acceleration.
Newton’s third law implies that action and reaction forces:
A act on the same body
B are equal in magnitude and opposite in direction and act on different bodies
C always cancel within a single body
D are always gravitational
Forces occur in pairs on different bodies.
A 5 kg block accelerates at 3 m/s². Net external force on it is:
A 15 N
B 8 N
C 2 N
D 0 N
F = ma = 5×3 = 15 N.
A block on an incline (angle θ) with no friction accelerates downwards with magnitude:
A g cosθ
B g sinθ
C g tanθ
D g
Component of gravity along plane is g sinθ.
Static friction differs from kinetic friction in that static friction:
A acts when surfaces are sliding
B acts to prevent relative motion up to μsN
C is always smaller than kinetic friction
D has units of m/s
Static friction resists initiation of slip up to a maximum μsN.
If two equal and opposite forces act on a rigid body at different points, they produce:
A only translation
B a couple (pure torque) with zero net force
C gravitational force
D no effect at all
Equal opposite non-collinear forces form a couple (torque).
A 10 kg box is pushed with 50 N across a horizontal floor; if kinetic friction is 30 N, net acceleration is:
A 2 m/s²
B 0.5 m/s²
C 3 m/s²
D 5 m/s²
Net F = 50 − 30 = 20 N; a = 20/10 = 2 m/s².
For a body in translational equilibrium, the vector sum of all forces is:
A maximum
B zero
C equal to weight
D equal to mass
Equilibrium requires ΣF = 0.
A person standing on a scale in an elevator accelerating upward with acceleration a reads:
A mg − ma
B mg + ma
C mg only
D ma only
Apparent weight N = m(g + a) when accelerating up.
In a non-inertial frame accelerating with acceleration a_frame, you must introduce a pseudo force on mass m equal to:
A +m a_frame (same direction as frame acceleration)
B −m a_frame (opposite direction)
C m g (downward)
D zero
Pseudo force in accelerating frame is −m a_frame.
The centrifugal force in a rotating (non-inertial) frame is:
A a real force exerted by the center
B a pseudo force directed outward from axis of rotation
C always tangential
D equal to zero for rotating observers
Centrifugal is apparent outward force in rotating frames.
Coriolis force on a moving object in a rotating frame is proportional to:
A mass × (angular velocity × velocity)
B position only
C mass times gravitational acceleration
D time squared
F_C = −2 m (Ω × v_rel).
In the Northern Hemisphere, an object moving northward is deflected to the:
A left
B right
C up
D down
Coriolis deflects motion to the right in Northern Hemisphere.
The Euler force appears when:
A frame has constant rotation rate
B rotation rate of the frame changes with time (dΩ/dt ≠ 0)
C frame translates uniformly
D gravity vanishes
Euler pseudo force = −m (dΩ/dt × r) when Ω changes.
If an object moves radially outward on a rotating disk, the Coriolis force acts:
A radially outward as well
B tangentially (perpendicular to radial motion)
C along rotation axis
D zero always
Coriolis = −2m(Ω × v); radial v gives tangential Coriolis.
Consider a car rounding a curve at constant speed. In the car’s accelerating frame, the apparent outward push felt by passengers is best described as:
A Coriolis force
B centrifugal pseudo force
C gravitational force
D normal force only
Centrifugal pseudo force appears outward in turning frame.
The net external force acting on a system equals the time rate of change of its:
A energy
B momentum of center of mass
C volume
D density
ΣF_ext = dP_cm/dt (center-of-mass momentum).
A 2 kg mass moving with velocity 3 m/s collides elastically with identical mass at rest. The moving mass after collision will have speed:
A 0 m/s
B 3 m/s
C 1.5 m/s
D 6 m/s
In a 1D elastic collision between equal masses, moving one stops and the other takes its speed.
Work done by friction over a distance is usually:
A positive (adds energy)
B negative (removes mechanical energy)
C zero always
D independent of path
Friction dissipates mechanical energy as heat.
The normal reaction on a body on a horizontal surface equals its weight when:
A the surface is frictionless and accelerating upward
B the system is in inertial frame and no vertical acceleration
C the body is accelerating upward
D the mass is changing
If no vertical acceleration, N = mg.
Two forces of magnitude 5 N and 12 N act at right angles. Resultant magnitude is:
A 7 N
B 13 N
C 17 N
D √(119) N
√(5² + 12²) = 13 N.
The impulse delivered by a force equals the change in:
A momentum
B kinetic energy
C potential energy
D velocity only
J = ∫F dt = Δp.
A block is attached to a spring and undergoes SHM. The restoring force is:
A proportional to displacement and opposite in direction (F = −kx)
B proportional to velocity
C constant always
D zero at all times
Hooke’s law: restoring force −k x.
In circular motion, if the speed doubles and radius remains same, centripetal force required becomes:
A unchanged
B double
C quadruple
D half
F_c ∝ v² → doubling v → 4× force.
For a mass sliding without friction on a rotating horizontal turntable, which pseudo force must be considered in the turntable frame?
A Coriolis only
B Centrifugal only (and Coriolis if particle moves relative to frame)
C Gravitational only
D Tension only
Centrifugal present for any point in rotating frame; Coriolis appears if particle has relative velocity.
A person walks across a uniformly accelerating truck bed (truck accelerating forward). From truck frame a backward pseudo force acts on the person equal to:
A −m a_truck (backward)
B +m a_truck (forward)
C mg (downward)
D zero
Pseudo force opposes frame acceleration.
The Coriolis acceleration has units of:
A m
B s⁻¹
C m/s²
D kg·m/s
It’s an acceleration (units m/s²).
Which of the following is conserved in absence of external torque?
A linear momentum only
B angular momentum about an axis
C kinetic energy always
D potential energy always
No external torque ⇒ angular momentum conserved.
A projectile fired long-range in the Northern Hemisphere must have its aim corrected because of:
A centrifugal force only
B Coriolis effect (deflection to right)
C no correction needed ever
D gravitational constant change
Coriolis causes lateral deflection of long-range projectiles.
An object attached to a string is whirled in a horizontal circle. If the string length halves and angular speed remains same, centripetal acceleration:
A halves
B doubles
C quadruples
D remains same
For constant angular speed ω, a_c = ω²r; halving r halves a_c.
Which force does no work on a particle moving freely in a rotating frame (assuming instantaneous velocity v_rel)?
A Coriolis force
B Centrifugal force
C Gravity
D Friction
Coriolis is perpendicular to velocity → does no work.
A railway carriage accelerating forward causes a hanging bob to deflect backward. The steady deflection angle θ satisfies:
A tanθ = a/g (where a is carriage acceleration)
B tanθ = g/a
C θ = 0 always
D θ = 90°
Equilibrium of real gravity mg and pseudo force m a gives tanθ = a/g.
A ship in Northern Hemisphere experiences Ekman transport (surface current) to the:
A left of wind direction
B right of wind direction
C toward equator only
D vertically downwards
Coriolis deflects flow to right in Northern Hemisphere; Ekman transport tends to the right of wind.
A puck slides on frictionless horizontal table toward the center of a turntable rotating CCW. In the rotating frame, the puck appears to be deflected:
A to the right (with respect to its motion)
B to the left
C straight inwards only
D upward
In CCW rotation, radial inward motion yields Coriolis deflection to the right of motion.
A small mass in free-fall inside an accelerating elevator (accelerating upward) experiences apparent gravity:
A g − a
B g + a
C only a
D zero
Apparent gravity increases by a when elevator accelerates upward.
The Coriolis parameter f = 2Ω sinφ depends on:
A Earth’s rotation rate Ω and latitude φ
B only latitude φ
C only Ω, not latitude
D altitude only
f combines Ω and sinφ.
A mass m on frictionless horizontal plane is attached to a string and whirled in circle. If speed increases, the required tension to maintain circular motion:
A decreases
B increases as v²/r
C remains constant
D equals mg
Tension provides centripetal F = m v²/r.
The force pair in Newton’s third law act on:
A the same body
B two different bodies
C the center of mass only
D a single point always
Action–reaction act on different bodies.
A driver turns the steering wheel to the right and feels thrown left. In the car’s non-inertial frame this perceived push is due to:
A friction only
B centrifugal pseudo force to the left
C Coriolis force to the right
D gravity change
In a turning frame passengers feel outward (centrifugal).
A rotating reference frame is non-inertial because observers fixed in it experience:
A no forces at all
B apparent (pseudo) forces like Coriolis and centrifugal
C only gravitational effects
D constant temperature
Rotation produces pseudo forces for fixed-frame observers.
A ball rolling on a rotating disk with no slipping will experience static friction that provides:
A tangential and/or radial forces necessary to maintain rolling without slip
B only normal force
C only gravity
D no forces at all
Static friction provides the tangential acceleration and can have radial component to prevent slipping.
For a particle moving north at speed v on Earth, Coriolis acceleration magnitude ≈:
A 2Ω v cosφ
B 2Ω v sinφ
C Ω v only
D v²/R
Horizontal Coriolis term involves 2Ω v sinφ.
A pendulum on a ship that accelerates forward will shift its equilibrium position. The new bob equilibrium angle θ from vertical satisfies:
A tanθ = a_ship/g
B tanθ = g/a_ship
C θ = 0
D θ = 90°
Balance between mg downward and pseudo m a backward gives tanθ = a/g.
A particle with position vector r in rotating frame experiences centrifugal acceleration equal to:
A Ω × (Ω × r)
B −2Ω × v
C −(dΩ/dt × r)
D g only
Centrifugal = Ω × (Ω × r) (per unit mass).
In the rotating frame, if the rotation axis points upward and a particle moves east, Coriolis force tends to:
A deflect it south or north depending on hemisphere
B change its mass
C do positive work always
D have no physical effect
Direction depends on geometry; eastward motion can have vertical Coriolis component depending on latitude.
A disc rotates with angular velocity Ω. A point on the rim at radius R has linear speed v =:
A Ω / R
B Ω R
C R / Ω
D Ω² R
v = ω r.
Which quantity remains unchanged when analyzing motion from an inertial frame compared to a properly corrected non-inertial frame?
A numerical values of pseudo forces
B physical predictions (trajectories, times) after including pseudo forces
C the sign of acceleration only
D the unit system only
Both frames give same physical results when pseudo forces are correctly included.
A freely moving object on Earth appears to curve when viewed from Earth because Earth is:
A non-rotating
B rotating (a non-inertial frame)
C stationary in space
D frictionless
Rotation makes surface frame non-inertial → apparent curvature via Coriolis.
A 3 kg block attached to a spring (k = 48 N/m) oscillates on frictionless surface. Its angular frequency ω is: