Relation Between Angular and Linear Quantities

Relation Between Angular and Linear Quantities MDCAT MCQs with answers

26 past paper MCQs on Relation Between Angular and Linear Quantities, from the Rotational and Circular Motion unit of MDCAT Physics. The year each question appeared is shown where known; tap “Show answer” for the correct option and a short solution.

Read the notes first Practise the unit as a quiz

1.A fighter plane is moving in a vertical circle of radius $r$. Its minimum velocity at the highest point of the circle will be: (MDCAT 2022)

  1. $\sqrt{3gr}$
  2. $\sqrt{2gr}$
  3. $\sqrt{gr}$
  4. $\sqrt{gr/2}$
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Correct answer: (c) $\sqrt{gr}$

At the least speed the weight alone supplies the centripetal force, so $mg=mv^2/r$ and $v=\sqrt{gr}$.

2.If a particle is moving with uniform circular motion, then: (MDCAT 2023)

  1. velocity and acceleration are antiparallel
  2. velocity and acceleration are parallel
  3. velocity and acceleration are perpendicular to each other
  4. the acceleration is zero
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Correct answer: (c) velocity and acceleration are perpendicular to each other

The speed does not change, so the acceleration is wholly centripetal and at right angles to the velocity.

3.On which car is a centripetal force acting? (MDCAT 2023)

  1. a car moving on a straight horizontal road
  2. a car moving at constant speed around a bend
  3. a car moving uphill at a constant velocity
  4. a car that is stationary
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Correct answer: (b) a car moving at constant speed around a bend

Only the car going round a bend has a curved path, and the force towards the centre of that curve is the centripetal force.

4.The centripetal acceleration of an object moving along a circle of radius $r$ with an angular speed $\omega$ is given by the formula: (MDCAT 2024)

  1. $a=r\omega^2$
  2. $a=r\omega$
  3. $a=\omega^2/r$
  4. $a=r/\omega^2$
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Correct answer: (a) $a=r\omega^2$

With $v=r\omega$, $a=v^2/r=r^2\omega^2/r=r\omega^2$.

5.A particle of mass $m$ moving on a circular path of radius $r$ with velocity $v$ has a centripetal force $F$ acting on it. If the velocity increases 2 times and the radius increases 4 times, the new centripetal force is: (MDCAT 2024)

  1. $2F$
  2. $F/2$
  3. $4F$
  4. $F$
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Correct answer: (d) $F$

$F=mv^2/r$, and $m(2v)^2/(4r)=4mv^2/(4r)=F$.

6.A roller coaster is moving with $30\ \mathrm{m\,s^{-1}}$ on a circular track of radius 30 m. If the net mass of coaster and passengers is $m$, the centripetal force acting on it is: (MDCAT 2024)

  1. $900m$
  2. $9m$
  3. $450m$
  4. $30m$
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Correct answer: (d) $30m$

$F=mv^2/r=m(30)^2/30=30m$.

7.If a particle moves along a circular path of radius r with angular displacement θ (in radians), then the arc length s is given by: (KMU MDCAT 2025)

  1. rθ
  2. r/θ
  3. θ/r
  4. 2πrθ
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Correct answer: (a) rθ

With the angle in radians the arc is $s=r\theta$.

8.In circular motion, if angular displacement is kept constant, decreasing the radius will: (SIBA MDCAT 2025)

  1. Increase linear displacement
  2. Increase linear velocity
  3. Decrease linear displacement
  4. Not affect linear displacement
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Correct answer: (c) Decrease linear displacement

With $s=r\theta$ and the angle fixed, a smaller radius gives a shorter arc.

9.The centripetal acceleration of an object moving along a circle of radius 'r' with an angular speed 'w' is given by the formula: (UHS MDCAT 2024)

  1. a = rw^2
  2. a = r ω
  3. a = r^2 ω
  4. A = r^2 ω^2
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Correct answer: (a) a = rw^2

With $v=r\omega$, the centripetal acceleration $v^2/r$ becomes $r\omega^2$.

10.A particle of mass 'm' is moving on a circular path of radius 'r' with velocity 'v', then centripetal force acting on it is F. If the velocity of particle increases by 2 times and radius of circular path increases by 4 times then new centripetal force F' will be; (UHS MDCAT 2024)

  1. F' = 2 F
  2. F' = 1/2 F
  3. F' = 4 F
  4. F' = F
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Correct answer: (d) F' = F

$F=mv^2/r$ gains a factor of four from the speed and loses four to the radius, so it is unchanged.

11.A roller coaster is moving with 30 ms-1 on a circular track of radius 30m. the net mass of coaster + passengers is 'm' the centripetal force acting on it is: (UHS MDCAT 2024)

  1. 900m
  2. m
  3. 450 m
  4. 30m
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Correct answer: (d) 30m

$F=mv^2/r=m\times900/30$, which is $30m$.

12.A car is moving in a circular path at a constant speed. What provides the necessary centripetal force to keep the car moving in this path? (KMU MDCAT 2024)

  1. The car's inertia resisting any change in direction
  2. The car's mass pulling it towards the centre of the circle
  3. The engine's power pushing the car forward
  4. The friction between the tyres and the road
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Correct answer: (d) The friction between the tyres and the road

The friction of the tyres on the road is the only inward force there is.

13.In a rotating spaceship, to produce artificial gravity, what does the centripetal force do? (KMU MDCAT 2024)

  1. Has no effect inside the spaceship
  2. Increases spaceship's rotation
  3. Pulls objects towards the centre
  4. Pushes the objects towards the outer wall
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Correct answer: (d) Pushes the objects towards the outer wall

The wall must push the occupant inwards, and by the third law they press outwards on it, which feels like weight.

14.When the mass of a body moving along a circle becomes half and radius becomes double, and v is constant, the centripetal force becomes? (KMU MDCAT 2024)

  1. Double
  2. Half
  3. One-fourth
  4. Remains Same
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Correct answer: (c) One-fourth

$F=mv^2/r$ loses a half to the mass and another half to the radius, so a quarter is left.

15.Which one provides centripetal force in a circular motion of a body? (SZABMU MDCAT 2023)

  1. Vertical component of weight
  2. Horizontal component of weight
  3. Weight of the body
  4. Force of friction
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Correct answer: (d) Force of friction

For a car on a level bend the friction of the tyres is the only inward force.

16.The tension is string at top of vertical circle is: (SZABMU MDCAT 2023)

  1. Zero
  2. mg
  3. 2mg
  4. 3mg
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Correct answer: (a) Zero

At the least speed that keeps the string taut, gravity alone supplies the centripetal force and the tension is zero.

17.The centripetal force in terms of angular velocity is given by: (SZABMU MDCAT 2023)

  1. F c = m r ω
  2. F c = m r ω^2
  3. F c = m r α^2
  4. F c = m r α
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Correct answer: (b) F c = m r ω^2

With $v=r\omega$, $mv^2/r$ becomes $mr\omega^2$.

18.In case of centripetal force the value of instantaneous acceleration is given by: (NUMS MDCAT 2023)

  1. ac = v/r
  2. ac = v2/r
  3. ac = vr
  4. ac = v2r
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Correct answer: (b) ac = v2/r

The centripetal acceleration is $v^2/r$, directed to the centre.

19.The centripetal force formula is: (NUMS MDCAT 2023)

  1. Fc = mω2
  2. Fc = mrω
  3. Fc = mrω2
  4. Fc = mr2ω
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Correct answer: (c) Fc = mrω2

With $v=r\omega$, $mv^2/r$ becomes $mr\omega^2$.

20.On which car there is resultant force? (UHS MDCAT 2023)

  1. Car moving on a straight horizontal road
  2. Car moving at constant speed around a bend
  3. Car moving uphill at a constant velocity
  4. Car that is stationary
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Correct answer: (b) Car moving at constant speed around a bend

A car on a bend is changing direction, so there is a resultant force towards the centre.

21.Centripetal force is provided by ______ in a frictional road around a circular path (PMC MDCAT 2022)

  1. Frictional force
  2. normal force
  3. gravitational force
  4. pseudo force
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Correct answer: (a) Frictional force

On a level road it is the friction of the tyres that turns the car.

22.The acceleration produced by the centripetal force is always: (PMC MDCAT 2022)

  1. Directed parallel to the center of the circle
  2. Directed perpendicular to the center of the circle
  3. Directed towards the center of the circle
  4. Directed away from the center of the circle
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Correct answer: (c) Directed towards the center of the circle

Centripetal acceleration points along the radius, towards the centre.

23.When an object experience circular motion, the direction of centripetal acceleration is: (NUMS MDCAT 2022)

  1. Towards center
  2. Along tangent
  3. Along the direction of motion
  4. Opposite of the direction of motion
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Correct answer: (a) Towards center

Centripetal acceleration points along the radius towards the centre.

24.A force which acts on an object moving in a circle and is directed towards the center of the circle is called: (PMC Practice 2021)

  1. Bending Force
  2. Centripetal Force
  3. Centrifugal force
  4. None of these
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Correct answer: (b) Centripetal Force

A force directed to the centre of the circle is the centripetal force.

25.If during circular motion, tangential velocity of a body becomes double, then centripetal force becomes: (PMC MDCAT 2020)

  1. Double
  2. One half
  3. Four times
  4. One fourth
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Correct answer: (c) Four times

$F=mv^2/r$ goes as the square of the speed.

26.Which of the following gives the relationship between linear velocity and angular velocity? (UHS MDCAT 2018)

  1. v = rω
  2. v = rθ
  3. v=sω
  4. v=sθ
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Correct answer: (a) v = rω

The linear velocity is the radius times the angular velocity.

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