13. Suppose you have an object tied to a rope and are rotating it over your head in uniform circular motion. If you increase the length of the rope, would you have to apply more or less force to maintain the same speed?

a. More force is required, because the force is inversely proportional to the radius of the circular orbit.

b. More force is required because the force is directly proportional to the radius of the circular orbit.

c. Less force is required because the force is inversely proportional to the radius of the circular orbit.

d. Less force is required because the force is directly proportional to the radius of the circular orbit.

To move an object at a constant speed after increasing the length of the rope, less force is required because the force is inversely proportional to the radius of the circular orbit. Thus option C is correct.

The force applied to the object moving in a circular motion can be given by:

From the equation, it is evident that force has been inversely proportional to the radius of the circular path. Since the length of the rope is doubled, the radius the circular path has also been doubled.

If we apply the same unit of force, the speed of the motion will increase, as speed has been directly proportional to the force applied.

Thus, to maintain the object at a constant speed, the force applied to the object has been reduced.

So, in order to move an object at a constant speed after increasing the length of the rope, less force is required because the force is inversely proportional to the radius of the circular orbit. Thus option C is correct.

For more information about the circular motion, refer to the link:

link

The correct option is (c).

Explanation:

When an object tied to a rope and we rotate it, the centripetal force acting on it. This force acts towards the center of the circle. The magnitude of the force is given by :

Where,

m is mass, v is speed and r is radius of path

If the length of the rope is increased, it means it will make a large circle i.e. large radius.

As we can see that force is inversely proportional to the radius of circle. It means less force is required because the force is inversely proportional to the radius of the circular orbit. Hence, the correct option is (c).

the answer is 12 as i may remember

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