Centripetal force Knowledge-Based Practice

Questions

1. 1.

   A rider remains pinned against the vertical inner wall of a cylindrical room rotating at a constant rate about its vertical axis after the floor drops. Which force provides the centripetal force acting on the rider?

   • A) The normal force exerted inward by the wall
   • B) The static frictional force exerted upward by the wall
   • C) The gravitational force exerted downward by Earth
   • D) The outward centrifugal force acting on the rider
2. 2.

   A small object of mass $m$ is attached to a light string of length $R$ and whirled in a vertical circle. What is the minimum speed the object must have at the highest point of its path to keep the string taut?

   • A) $v = \sqrt{2gR}$
   • B) $v = 2\sqrt{gR}$
   • C) $v = gR$
   • D) $v = \sqrt{gR}$
3. 3.

   A roadway is banked at an angle $\theta$ relative to the horizontal so that a vehicle can negotiate a curve of radius $r$ at speed $v$ with zero friction. Which of the following expressions correctly gives the required banking angle $\theta$?

   • A) $\tan \theta = \frac{v^2}{rg}$
   • B) $\sin \theta = \frac{v^2}{rg}$
   • C) $\tan \theta = \frac{rg}{v^2}$
   • D) $\cos \theta = \frac{v^2}{rg}$
4. 4.

   A car travels around a flat, unbanked circular curve of radius $r$. If the coefficient of static friction between the tires and the road is $\mu_s$ and the acceleration due to gravity is $g$, which expression gives the maximum speed the car can maintain without skidding?

   • A) $v = \mu_s g r$
   • B) $v = \sqrt{\mu_s g r}$
   • C) $v = \sqrt{\frac{\mu_s g}{r}}$
   • D) $v = \sqrt{\frac{g r}{\mu_s}}$
5. 5.

   Two objects of equal mass undergo uniform circular motion along paths of the same radius. If the period of revolution of the first object is half that of the second object, what is the ratio of the net centripetal force on the first object to that on the second object?

   • A) 1/4
   • B) 1/2
   • C) 2
   • D) 4
6. 6.

   A roller coaster car of mass $m$ moves at speed $v$ through the lowest point of a vertical circular track of radius $r$. Which expression represents the magnitude of the normal force exerted by the track on the car at this point?

   • A) $mg - \frac{mv^2}{r}$
   • B) $\frac{mv^2}{r}$
   • C) $mg + \frac{mv^2}{r}$
   • D) $mg$
7. 7.

   An object attached to a string moves at a constant speed in a horizontal circle on a frictionless surface. If the string suddenly breaks, how does the object move immediately after the break?

   • A) It moves radially outward along the line extending from the center of the circle.
   • B) It moves in a straight line tangent to the circle at the point of release.
   • C) It follows a curved, spiral path that gradually widens away from the center.
   • D) It continues along the circular path for a short distance before stopping.
8. 8.

   Which statement best describes the centripetal force acting on an object undergoing uniform circular motion?

   • A) It is the net force directed toward the center of the circle that continuously alters the direction of the object's velocity.
   • B) It is an outward force created by inertia that balances the inward acceleration of the object.
   • C) It is an independent fundamental force that acts in addition to real forces like tension or gravity.
   • D) It is a tangential force directed along the path that continuously changes the object's kinetic energy.
9. 9.

   Which of the following statements correctly describes the work done by the centripetal force on an object undergoing uniform circular motion?

   • A) The work done is positive because the centripetal force acts in the direction of the object's acceleration.
   • B) The work done is zero because the centripetal force is always perpendicular to the instantaneous displacement.
   • C) The work done is equal to the kinetic energy of the object because the force continuously maintains its speed.
   • D) The work done is negative because the centripetal force acts opposite to the direction of motion.
10. 10.

    A car of mass $m$ travels at a constant speed $v$ around a flat circular track of radius $r$. If the car's speed is doubled while the track's radius is halved, by what factor does the required centripetal force change?

    • A) It increases by a factor of 2.
    • B) It increases by a factor of 8.
    • C) It increases by a factor of 4.
    • D) It remains unchanged.

Answers and step-by-step solutions appear after you finish the test.