This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Non-Uniform Circular Motion”.
1. A stone tie with a string held at one end is being rotated at a constant angular velocity in the air. The tangential velocity will remain constant if _______
a) The plane of motion of the stone is parallel to the ground
b) The plane of motion of the stone is perpendicular to the ground
c) The plane of motion of the stone is at an angle of 45 degrees to the ground
d) The tangential velocity is independent of the plane of motion
Explanation: When the plane motion of the stone is parallel to the ground, the tangential velocity experiences acceleration in two directions, one towards the centre and other towards the ground. Both these directions are perpendicular to the direction of the tangential velocity. Hence the tangential velocity will not change.
2. A ball tied at the end of a perfect string tied tightly (assume fixed) to a wooden bar at the other end is rotating with constant angular velocity. Its tangential velocity will _______
a) Increase with time
b) Decrease with time
c) Will remain constant
d) Will decrease exponentially
Explanation: As the other end of the string is fixed to the wooden bar, the motion will cause the string to wrap itself around the bar. This will result in decrease in the effective radius of the circular motion. Tangential velocity v = ωr, the tangential velocity will decrease with time.
3. A rocket takes off from the earth and continues to move in a circular orbit with the thrusters on. What can be said about the angular velocity of the rocket?
a) It increases
b) It decreases
c) It remains constant
d) It changes abruptly
Explanation: When the rocket is in the orbit with the thrusters on, there is a tangential force that the rocket experiences. This force will result in increasing the tangential velocity. Since the angular velocity is directly proportional to the tangential velocity, the angular velocity will also increase.
4. The radius of a body moving in a circle with constant angular velocity is given by r = 4t2, with respect to time. What is the magnitude of the tangential velocity at t = 2s, if the angular velocity is 7 rad/s?
Explanation: The tangential velocity is given as v = ωr. At t = 2s, r = 16 units. The angular velocity is 7 rad/s. Hence, the tangential velocity, v = 7 x 16 = 112 units/s.
5. A car moving around a tree has the distance from the tree defined as r = 5t2 + 7. What is the magnitude of the centripetal acceleration at t = 2s, if the angular velocity is 2 rad/s.
Explanation: The centripetal acceleration is given as ac = rω2. Here, we have r = 5t2 + 7 = 27 units at t = 2s. Angular velocity is 2 rad/s. On substituting all the values, we get, the acceleration as 108 units/s2.
6. The tangential velocity in a circular motion change as v = 2t2 – 7 with the radius being equal to 3 m. What is the angular velocity at t = 1 s in rad/s?
Explanation: The angular velocity is given as, ω = v/r. Hence, the function for angular velocity is ω = (2t2 – 7)/3. On substituting, the suitable values, we will get the angular velocity as -5/3 rad/s.
7. The tangential velocity of a body in a non-uniform circular motion varies as v = 7t2 – 2v with the radius being equal to 21 m. What is the angular acceleration at t = 2 s in rad/s2?
Explanation: The angular velocity is given as, ω = v/r. Hence, the function for angular velocity is ω = (7t2 – 2)/21. On differentiating this expression, we will get the angular acceleration as t2/3 On substituting, the suitable values, we will get the angular acceleration as 4/3 rad/s2.
8. Which of the following is a suitable word to describe the motion of a rotating ball tied to rope tied tightly to a fixed support?
a) Spiral motion
b) Circular motion
c) Elliptic motion
d) Uniform motion
Explanation: A ball, tied to a rope, rotating around a fixed support will cause the rope to wind itself around the support. Hence, the motion will be circular with decreasing radius. This motion will cause the path look like a spiral. Hence the motion is spiral in nature.
9. A block of mass 5 Kg, exhibits circular motion with the mass decreasing at the rate of 0.5 Kg/s. At what time the centripetal force will be zero on the block?
a) At 10 s
b) At 5 s
c) At 1 s
d) At 7 s
Explanation: The centripetal force on a body is directly proportional to its mass with a proportionality constant of 1. Hence the centripetal force will be zero when the mass is zero. The function for the mass at t seconds is m = 5 – 0.5t. On equating this to zero we get, t = 10 s. this is the required time.
10. A box of mass 10 Kg, moves in circular motion with the mass function as m = 7t. The function for the radius is r = 2t2. By what factor does the centripetal force exceed the square of the tangential velocity at t = 2 s?
Explanation: The centripetal force on a body is given as Fc = mv2/r. Hence, the required factor is the ratio of the mass to the radius at t = 2s. Hence, required factor = m/r = 7/2t. On substituting the values, we get the factor as 7/4.
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