CBSE Class 9 Science Advanced Physics Circular Motion MCQs Set 01

Answer: (a) 57.3º

Explanation:
1. The symbol c stands for radian, so 1^c means 1 radian.
2. 2π radian = 360º, so 1 radian = 360º ÷ 2π = 57.3º.
3. The answer is (A).

Teacher's Note:
1. Remember that a full circle is 2π radian.
2. Dividing 360º by 2π (about 6.28) gives roughly 57.3º.

Answer: (b) π/12

Explanation:
1. The earth turns through 2π radian in 24 hours.
2. ω = 2π ÷ 24 = π/12 rad/hr.
3. The answer is (B).

Teacher's Note:
1. Use ω = 2π/T with T in hours, because the answer is wanted in rad/hr.
2. Do not convert the period into seconds here.

Answer: (b) π/1800 rad/s

Explanation:
1. The minute hand completes one turn in 60 min = 3600 s.
2. ω = 2π ÷ 3600 = π/1800 rad/s.
3. The answer is (B).

Teacher's Note:
1. The period of the minute hand is one hour.
2. Always change the period to seconds when the unit asked is rad/s.

Answer: (c) in accelerated motion

Explanation:
1. The speed is constant, but the boy moves on a circle, so the direction of velocity keeps changing.
2. A changing velocity means acceleration.
3. So the boy is in accelerated motion, option (C).

Teacher's Note:
1. Velocity needs both speed and direction to stay the same.
2. Constant speed on a curve does not mean constant velocity.

Answer: (a) 30π

Explanation:
1. Radius r = 0.5 m. One revolution is a distance 2πr = π m.
2. Speed = 30 × π = 30π m/s.
3. (Using ω = 2π × 30 = 60π rad/s, v = ωr = 60π × 0.5 = 30π m/s.)
4. The answer is (A).

Teacher's Note:
1. Diameter is given, so halve it to get the radius.
2. Distance in one turn times turns per second gives the speed.

Answer: (b) Variable acceleration

Explanation:
1. In uniform circular motion the size of the acceleration stays the same, but its direction (towards the centre) keeps turning.
2. A vector that changes direction is not constant, so the acceleration is variable, option (B).

Teacher's Note:
1. Constant acceleration needs both size and direction fixed.
2. The acceleration always points to the centre, and the centre direction changes as the body moves.

Answer: (c) angular acceleration

Explanation:
1. Angular acceleration α = change in ω ÷ time.
2. So the rate of change of angular velocity is angular acceleration.

Teacher's Note:
1. Compare with linear motion: rate of change of velocity is acceleration.
2. Put the word angular in front of each quantity.

Answer: (c) 1 : 720

Explanation:
1. Hour hand: T = 12 h = 43200 s. Second hand: T = 60 s.
2. ω is proportional to 1/T, so ω_hour : ω_second = 60 : 43200 = 1 : 720.

Teacher's Note:
1. Angular speed is inversely proportional to the time period.
2. Write both periods in the same unit first.

Answer: (d) 4π

Explanation:
1. 120 revolutions/minute = 2 revolutions/second.
2. ω = 2π × 2 = 4π rad/s.

Teacher's Note:
1. Change revolutions per minute to per second by dividing by 60.
2. Each revolution is 2π radian.

Answer: (d) rad/s

Explanation:
1. Angular velocity = angle ÷ time, so its unit is radian per second.
2. The answer is (D); rad is the unit of angle and rad/s² is for angular acceleration.

Teacher's Note:
1. Match each unit with its quantity: rad for angle, rad/s for ω, rad/s² for α.
2. m/s is the unit of linear speed.

Answer: (a) 1 : 2

Explanation:
1. Same time for one circle means the same period, so the same ω.
2. v = ωr, so v₁ : v₂ = r₁ : r₂ = 1 : 2.

Teacher's Note:
1. When the period is equal, speed is proportional to radius.
2. The bigger circle has to be covered at a higher speed.

Answer: (b) 10

Explanation:
1. ω = v ÷ r = 10 ÷ 1 = 10 rad/s.
2. The mass of 2 kg is not needed.

Teacher's Note:
1. Some data in a question is only there to distract you.
2. Use ω = v/r.

Answer: (a) \( \omega = \frac{v}{r} \)

Explanation:
1. For circular motion the arc covered is x = rθ.
2. Dividing by time gives v = rω, so ω = v/r.
3. The answer is (A).

Teacher's Note:
1. Always check the units: v/r gives m/s ÷ m = 1/s.
2. The formula v = rω is the one to remember.

Answer: (a) a constant speed

Explanation:
1. A body in uniform circular motion has constant speed, so (A) is possible.
2. Velocity cannot be constant because its direction changes, so (B) is wrong.
3. The velocity is always along the tangent, so (C) is wrong, and there is always an acceleration towards the centre, so (D) is wrong.

Teacher's Note:
1. Test each option with uniform circular motion in mind.
2. Speed can stay fixed, velocity cannot.

Answer: (c) along the radius

Explanation:
1. For uniform circular motion the acceleration points towards the centre of the circle, that is, along the radius.
2. The answer is (C).

Teacher's Note:
1. The tangent is the direction of velocity, not of acceleration.
2. The key takes the motion as uniform, where there is no tangential part.

Answer: (c) 3.4 cm/s²

Explanation:
1. ω = 2π ÷ (24 × 3600) = 7.27 × 10^–5 rad/s; R = 6.4 × 10⁶ m.
2. a = ω²R = (7.27 × 10^–5)² × 6.4 × 10⁶ = 3.4 × 10^–2 m/s².
3. In cm/s²: 3.4 cm/s², option (C).

Teacher's Note:
1. Change km to m and hours to seconds before substituting.
2. Do not forget the last step: m/s² to cm/s² multiplies by 100.

Answer: (a) Circular

Explanation:
1. Every point of the rim stays at the same distance from the axis, so it moves on a circle.
2. The motion is circular.

Teacher's Note:
1. The axis is fixed, so the wheel does not move forward.
2. A rolling wheel on a road would be different.

Answer: (d) all of them

Explanation:
1. Each case moves along a circle with constant speed.
2. So all three are examples, option (D).

Teacher's Note:
1. Uniform means constant speed along the circle.
2. Orbits are treated as nearly circular here.

Answer: (c) π

Explanation:
1. A full circle subtends 2π radian at the centre.
2. A semicircle is half of it, so the angle is π (180º).

Teacher's Note:
1. Half of 2π is π.
2. A semicircle is the same as a straight diameter at the centre, 180º.

Answer: (b) 5 m/sec²

Explanation:
1. Centripetal (radial) acceleration = v²/r = 20² ÷ 100 = 4 m/s².
2. Tangential acceleration (from speeding up) = 3 m/s².
3. These two are at right angles, so a = √(4² + 3²) = √25 = 5 m/s².

Teacher's Note:
1. Add the two accelerations as vectors at right angles, not as plain numbers.
2. The 3-4-5 triangle makes the sum easy.

Answer: (a) \( \frac{r_2}{r_1} \)

Explanation:
1. Centripetal force F = mv²/r.
2. m and v are the same for both, so F is proportional to 1/r.
3. F₁ : F₂ = 1/r₁ : 1/r₂ = r₂ : r₁, that is \( \frac{r_2}{r_1} \), option (A).

Teacher's Note:
1. With speed fixed, a smaller circle needs a bigger force.
2. Invert the radii ratio.

Answer: (a) R / r

Explanation:
1. Same period means the same ω.
2. Centripetal acceleration a = ω²r, so a is proportional to the radius.
3. a₁ : a₂ = R : r, option (A).
4. The masses do not matter for acceleration.

Teacher's Note:
1. Use a = ω²r when ω is equal and a = v²/r when v is equal.
2. Mass cancels out when we talk about acceleration.

Answer: (c) 12 : 1

Explanation:
1. Minute hand period = 1 h; hour hand period = 12 h.
2. ω is proportional to 1/T, so ratio = 12 : 1.
3. The answer is (C).

Teacher's Note:
1. The faster hand has the larger angular speed.
2. The minute hand turns 12 times while the hour hand turns once.

Answer: (c) 1000 N

Explanation:
1. v = 36 km/h = 36 × 1000 ÷ 3600 = 10 m/s.
2. F = mv²/r = 500 × 10² ÷ 50 = 1000 N.

Teacher's Note:
1. Change km/h into m/s before using the formula (divide by 3.6).
2. Centripetal force is mass times v² over r.

Answer: (b) directed towards the centre of the circle

Explanation:
1. The word centripetal means centre-seeking.
2. The acceleration always points towards the centre.

Teacher's Note:
1. Away from the centre would be centrifugal.
2. It is at right angles to the velocity.

Answer: (c) υ²/r

Explanation:
1. The centripetal acceleration is a = v²/r, where v is the speed.
2. So the answer is (C).

Teacher's Note:
1. Check units: (m/s)² ÷ m = m/s².
2. Here the speed is written with the symbol υ, which means the same as v.

Answer: (b) \( \frac{2\pi R}{t} \)

Explanation:
1. Diameter = 2R, so the radius is R.
2. Distance in one round = circumference = 2πR.
3. Speed = distance ÷ time = \( \frac{2\pi R}{t} \), option (B).

Teacher's Note:
1. Do not use the area πR² for distance.
2. Speed has the unit of length over time.