Question

To double the orbital speed ${\text{V}}$ and halve the angular velocity $\omega $. The centripetal acceleration of a revolving body:
A) Is quadrupled
B) Remains unchanged
C) Is halved
D) Is doubled

Answer 1

Hint: If the orbital speed is doubled, $v' = 2v$ and angular velocity is halved,
New centripetal acceleration becomes: so, the new centripetal acceleration is the same as the initial acceleration.

Complete step by step answer:
The centripetal force if the speed is doubled, when the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times force to stay the motion during a circle.
The SI composite unit of angular speed is the radian per second.
The centripetal acceleration if speed is doubled , the force required to provide the centripetal acceleration would be 4 times.
Therefore the orbital speed ${\text{V}}$ is doubled and the angular velocity $\omega $ is halved when the centripetal acceleration of the revolving body is quadrupled.

So, option (A) is the correct answer.

Additional Information:
A change in velocity is understood as acceleration. The change in velocity thanks to circular motion is understood as acceleration. Centripetal acceleration can be calculated by taking the radius of the circle the object is traveling along.

Note: Just a couple of examples are, the strain within the rope on a tether ball, the force of earth’s gravity on the moon, friction between roller skates and a rink floor, a banked roadway’s forces on the tube of a spinning centrifuge. Any net force causing uniform circular motion is called a force.