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Life is full of circular motion. Planets move in a round orbit around the sun. An automobile going around a bend shrieking is also in circular motion. If you’ve ever played lawn tennis, which involves a ball on a string flying around a pole, you’ve seen another example of circular motion. The motion is considered to be uniform if you’re travelling around in a circle at a consistent pace.
Motion in a circle at a constant speed is known as uniform circular motion. This is due to a centripetal force, which is a force that points towards the centre of a circle. An item in uniform circular motion has a net force towards the round’s centre, an acceleration vector towards the circle’s centre, and a velocity tangent to the circle, according to mathematics.
1. ______ is the force that maintains the body moving in a circular manner.
a) Centripetal force
b) Centrifugal force
c) Force of gravity
d) Reaction forces
Answer: a
Explanation: The centripetal force is what keeps bodies moving in a circular direction. The centripetal force is related to the tangential velocity squared and inversely proportional to the radius of the circle.
2. Mathematical expression for centripetal force is ______
a) mv²/r
b) mv/r
c) v²/r
d) mv³/r
Answer: a
Explanation: The centripetal force is related to the tangential velocity squared and inversely proportional to the radius of the circle. As a result, when we calculate the formula, we obtain mv²/r.
3. What is the centripetal acceleration of a body having a mass of 10 kg travelling at a speed of 5 m/s in a circle with a radius of 5 m?
a) 5m/s²
b) 25m/s²
c) 0.5 m/s²
d) 50 m/s²
Answer: a
Explanation: mv²/r is the formula for centripetal force. As a result, v²/r equals the centripetal acceleration. v = 5 and r = 5 in this case. As a result, after solving, the centripetal acceleration will be 5m/s²
4. The centrifugal force always works in one of the following directions:
a) Towards the centre
b) Away from the centre
c) In tangential direction
d) Outside of the plane of motion
Answer: b
Explanation: The centrifugal force always operates away from the body’s movement’s centre. The centripetal force, on the other hand, constantly works towards the circle’s centre, keeping the body moving in the circle.
5. A ball is rotating in a circle with a radius of 5 metres and a constant tangential velocity of 20 metres per second. A stone is also rotating with a constant tangential velocity of 16 m/s in a circle with a radius of 4 m. Which of the following statements regarding both circular movements is correct?
a) Both have same angular velocity
b) Both have different angular velocity
c) Angular velocity of ball > angular velocity of stone
d) Angular velocity of stone > angular velocity of ball
Answer: a
Explanation: Angular velocity = ω = r × v / |r|²
When we compute the angular velocities for each circular motion, we observe that the angular velocities are identical and the value is 4 rad/s.
6. A rotating stone has an angular velocity of 11 rad/s. In 0.5 seconds, how much angular displacement is covered?
a) 5.5 rad
b) 0.55 rad
c) 55 rad
d) 0.5 rad
Answer: a
Explanation: The rate of change of angular displacement is known as angular velocity. The angular velocity is 11 rad/s in this case. This means that the stone rotates by 11 degrees in one second. As a result, it will traverse an angular displacement of 5.5 rad in 0.5 seconds.
7. A body moves vertically in a circular manner. It is not subjected to which of the following forces?
a) Force of gravity
b) Centripetal force
c) Normal reaction force
d) Centrifugal force
Answer: c
Explanation: When a body moves in a vertical circular motion, it is subjected to four forces: centripetal force, centrifugal force, gravity, and resistance provided by the medium. Apart from these, it is not subjected to any additional forces under typical circumstances.
8. A body with a mass of 2 kg and a weight of 20 N is travelling in a vertical circular motion with a radius of 1 m and a velocity of 2 m/s. What is the lowest point in the string’s tension?
a) 28 N
b) 20 N
c) 8 N
d) 15 N
Answer: a
Explanation: The body feels centrifugal force and weight in the same direction at the lowest position, which is opposing the direction of tension in the string. mv²/r = 8 N may be used to compute centrifugal force. As a result, the tension is equal to the weight multiplied by the centrifugal force, which equals 28 N.
9. A body with a mass of 2 kg and a weight of 20 N is travelling in a vertical circular motion with a radius of 1 m and a velocity of 5 m/s. What is the highest point in the string’s tension?
a) 30 N
b) 50 N
c) 20 N
d) 25 N
Answer: a
Explanation: The tension and weight are in the same direction at the highest point, while the centrifugal force is in the opposite direction. mv²/r = 50 N may be used to compute centrifugal force. As a result, the tension is equal to the product of the centrifugal force and the weight, which is 30 N.
10. A body with a mass of 2 kg and a weight of 20 N is travelling in a vertical circular motion with a radius of 1 m and a velocity of 5 m/s. When the string is horizontal, what is the tension?
a) 30 N
b) 50 N
c) 20 N
d) 25 N
Answer: b
Explanation: When the string is horizontal, the tension in the string and the centrifugal force are in opposition to one another. mv²/r = 50 N may be used to compute centrifugal force. As a result, the tension equals the centrifugal force, which is 50 N.
11. Which of the following devices is based on the circular motion principle?
a) Centrifuge
b) Screw Gauge
c) Ruler
d) Vernier callipers
Answer: a
Explanation: The centrifuge makes use of the centrifugal force generated by circular motion. Platelets are often separated from blood samples using a centrifuge. It’s a crucial piece of equipment for blood research. Other centrifuge versions include cream separators and other similar machines.
12. At which point in a vertical circular motion is the string tension at its lowest?
a) At the highest position
b) At the lowest position
c) When the string is horizontal
d) At an angle of 35° from the horizontal
Answer: a
Explanation: When the body is at its maximum point of motion, the answer is a. This is because the tension equals the centrifugal force minus the weight at the greatest point. This is the smallest amount of tension that can be maintained during the action.
