Centripetal force Knowledge-Based Download PDF

Questions

1. 1.

   A car of mass $m$ travels at a constant speed $v$ over the crest of a vertical circular hill of radius $R$. Taking the acceleration due to gravity as $g$, which expression gives the magnitude of the normal force $N$ exerted by the road on the car at the highest point of the hill?

   • A) $N = m g + \frac{m v^2}{R}$
   • B) $N = \frac{m v^2}{R}$
   • C) $N = m g - \frac{m v^2}{R}$
   • D) $N = \frac{m v^2}{R} - m g$
2. 2.

   A bob of mass $m$ suspended from a light string moves at a constant speed in a horizontal circle such that the string maintains a constant angle $\theta$ with the vertical. Taking the acceleration due to gravity as $g$, what is the magnitude of the net centripetal force acting on the bob?

   • A) $mg \cos\theta$
   • B) $mg \sin\theta$
   • C) $\frac{mg}{\cos\theta}$
   • D) $mg \tan\theta$
3. 3.

   An object of mass $m$ moves at a constant speed along a circular track of radius $r$, completing one full revolution in a period $T$. Which expression gives the magnitude of the net centripetal force acting on the object?

   • A) $\frac{2\pi m r}{T}$
   • B) $\frac{4\pi m r^2}{T^2}$
   • C) $\frac{4\pi^2 m r}{T^2}$
   • D) $\frac{2\pi^2 m r}{T^2}$
4. 4.

   A roller-coaster car moves along a vertical circular loop of radius $R$. Taking the acceleration due to gravity as $g$, what is the minimum speed the car must have at the highest point of the loop to maintain contact with the track?

   • A) $\sqrt{gR}$
   • B) $\sqrt{2gR}$
   • C) $gR$
   • D) $\frac{1}{2}gR$
5. 5.

   A small puck attached to a string moves at a constant speed in a horizontal circle on a frictionless table. If the string suddenly breaks, which path does the puck follow immediately after the break?

   • A) A straight line tangent to the circular path at the point where the string broke
   • B) A straight line directed radially outward away from the center of the circle
   • C) A curved path that spirals outward with increasing radius
   • D) A straight line directed radially inward toward the center of the circle
6. 6.

   A vehicle travels at constant speed around a horizontal circular turn on a frictionless road banked at an angle to the horizontal. Which force component provides the centripetal acceleration keeping the vehicle on this circular path?

   • A) The component of the gravitational force directed parallel to the incline
   • B) The horizontal component of the normal force exerted by the road
   • C) The vertical component of the normal force exerted by the road
   • D) The component of the gravitational force perpendicular to the banked road
7. 7.

   A small stone of mass $m$ attached to a light string of length $L$ moves in a vertical circle. What is the magnitude of the tension $T$ in the string when the stone passes through the lowest point of its path with instantaneous speed $v$?

   • A) $T = mg + \frac{mv^2}{L}$
   • B) $T = \frac{mv^2}{L} - mg$
   • C) $T = \frac{mv^2}{L}$
   • D) $T = mg$
8. 8.

   A car travels at a constant speed along a flat, unbanked circular curve. Which force provides the centripetal acceleration that keeps the car on this circular path?

   • A) The upward normal force exerted by the road surface
   • B) The static friction force exerted inward by the road on the tires
   • C) The kinetic friction force acting opposite to the car's forward velocity
   • D) The downward gravitational force acting on the car
9. 9.

   An object moves at a constant speed along a circular path. What is the direction of the centripetal force acting on the object, and what effect does this force have on the object's speed?

   • A) It points radially outward from the center, continuously decreasing the speed of the object.
   • B) It points toward the center of the path perpendicular to velocity, changing only the direction of motion while leaving the speed unchanged.
   • C) It points tangent to the path in the direction of motion, increasing the speed to keep the object moving in a circle.
   • D) It points opposite to the direction of motion, maintaining a constant speed by counteracting inertia.
10. 10.

    A small object moves with a constant speed $v$ along a circular path of radius $r$, experiencing a centripetal force of magnitude $F$. If the speed of the object is doubled and the radius of the circular path is quadrupled while its mass remains constant, what is the new magnitude of the centripetal force?

    • A) $0.5F$
    • B) $F$
    • C) $2F$
    • D) $4F$