Dynamics of uniform circular motion, centripetal force and applications including vehicles on level and banked roads - One Line Questions

1. A particle moves in a circle of radius 0.5 m with a constant speed of 2 m/s. What is the magnitude of its centripetal acceleration? — 4 m/s^2
2. What is the formula for centripetal acceleration (a_c)? — a_c = v^2 / r
3. The centripetal force is provided by a real interaction between objects. — Always
4. A string breaks when the tension exceeds a certain limit. If a mass tied to a string is whirled in a horizontal circle, at what point is the tension maximum for a given speed and radius? — The tension is constant throughout the motion
5. If a car travels at a speed lower than the design speed on a banked road, which force helps prevent skidding inwards? — Static friction acting outwards
6. When a cyclist leans inwards while turning, the horizontal component of the normal force provides the: — Centripetal force
7. If a car travels at a speed higher than the design speed on a banked road, which force helps prevent skidding outwards? — Static friction acting inwards
8. What is the term for the fictitious force experienced by an observer in a rotating frame of reference, which appears to push objects outwards? — Centrifugal force
9. What is the defining characteristic of uniform circular motion? — Constant speed and changing direction
10. The apparent weight of a person in a vehicle moving on a convex circular path (like a flyover) at the highest point is: — Less than their actual weight
11. The apparent weight of a person in a vehicle moving on a concave circular path (like the bottom of a well) at the lowest point is: — More than their actual weight
12. What is the formula for centripetal force (F_c)? — F_c = mv^2 / r
13. For a vehicle moving on a banked road at a specific design speed, the centripetal force is provided solely by the horizontal component of the: — Normal force
14. If the speed of an object in uniform circular motion is doubled, the centripetal force required is: — Quadrupled
15. If the radius of the circular path is halved, while speed remains constant, the centripetal force required is: — Doubled
16. If the radius of a satellite's orbit increases, its orbital speed: — Decreases
17. The speed of a satellite in a circular orbit around the Earth depends on: — The radius of the orbit and the mass of the Earth
18. The centripetal force is the force required to: — Keep an object moving in a circular path
19. The unit of angular velocity is: — radians per second (rad/s)
20. If a satellite of mass 'm' orbits the Earth of mass 'M' at a radius 'r' with speed 'v', the relation is: — mv^2 / r = GMm / r^2
21. In the case of a car turning on a level road, the centripetal force is provided by static friction. If the speed is too high, the static friction reaches its maximum value (μ_s * N), and the car skids. This implies: — mv^2 / r > μ_s * mg
22. For a vehicle moving on a convex flyover of radius 'r' at speed 'v', the normal force from the flyover at the highest point is given by: — N = mg - mv^2 / r
23. For a vehicle moving on a concave path (like the bottom of a well) of radius 'r' at speed 'v', the normal force from the path at the lowest point is given by: — N = mg + mv^2 / r
24. When a road is banked, the centripetal force is provided by: — Only the normal force
25. In the context of a car turning on a level road, if the speed exceeds v_max, the car will: — Skid outwards
26. To safely cross a convex flyover of radius 'r' at speed 'v', the speed 'v' must be less than: — sqrt(g * r)
27. What is the minimum speed required for a stunt pilot to loop-the-loop in a vertical circle of radius 'r' without the plane falling? — sqrt(g * r)
28. For a conical pendulum with string length L and angle θ with the vertical, what is the time period of revolution? — T = 2π sqrt(L cos(θ) / g)
29. In a vertical circular motion, the tension in the string at the highest point is: — T = mv^2 / r - mg
30. In a vertical circular motion, the tension in the string at the lowest point is: — T = mv^2 / r + mg
31. What is the condition for a vehicle to safely negotiate a banked turn at the design speed (v) without relying on friction? — tan(θ) = v^2 / (g * r)
32. For a cyclist leaning at an angle θ with the vertical to negotiate a turn of radius r at speed v, the relationship is: — tan(θ) = v^2 / (g * r)
33. For an object undergoing uniform circular motion, the centripetal force is directed: — Radially inwards towards the center
34. In the motion of a satellite orbiting the Earth in a circular path, the centripetal force is provided by: — The gravitational force between the Earth and the satellite
35. What provides the centripetal force when a car turns on a level road? — The force of static friction between tires and road
36. A cyclist turns on a level road. The centripetal force is provided by: — The friction between the tires and the road
37. In the context of a conical pendulum, the bob moves in a horizontal circle. What provides the centripetal force? — The horizontal component of tension
38. What is the purpose of banking a road at a turn? — To provide the necessary centripetal force
39. In uniform circular motion, the velocity vector is always directed: — Along the tangent to the circle
40. Centrifugal force is a real force acting on the object. — False, it is a fictitious force experienced in a non-inertial frame.
41. If a vehicle turns on a circular path with a constant speed, it is undergoing: — Non-uniform acceleration
42. What is the speed of a satellite in a circular orbit of radius 'r' around a planet of mass 'M'? — v = sqrt(GM / r)
43. The angular velocity (ω) of an object in uniform circular motion is related to its speed (v) and radius (r) by: — v = ω * r
44. Consider a mass 'm' moving in a vertical circle of radius 'r' with speed 'v'. What is the condition for the mass to complete the circle? — v at the top must be >= sqrt(g * r)
45. If a car takes a turn on a road banked at an angle θ, and the speed is such that friction is not required, then tan(θ) is equal to: — v^2 / (rg)
46. What is the maximum safe speed for a vehicle on a banked road with banking angle θ and coefficient of static friction μ_s? — v_max = sqrt(g * r * (μ_s + tan(θ)) / (1 - μ_s * tan(θ)))
47. What is the maximum speed a car can take a turn of radius 'r' on a level road without skidding, if the coefficient of static friction is 'μ_s'? — v_max = sqrt(μ_s * g * r)
48. What is the minimum safe speed for a vehicle on a banked road with banking angle θ and coefficient of static friction μ_s? — v_min = sqrt(g * r * (tan(θ) - μ_s) / (1 + μ_s * tan(θ)))
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