On a frictionless banked road, the angle of banking for a curve of radius r and a speed v is given by the tangent of the angle equal to:
- A.v squared divided by r g
- B.r g divided by v squared
- C.v divided by r g
- D.v squared multiplied by r g
Correct answer
Explanation
The correct answer is A, v squared divided by r g. On a banked road the normal reaction is tilted, its vertical component balances the weight and its horizontal component supplies the centripetal force; dividing one equation by the other leaves the tangent of the banking angle equal to the square of the speed divided by the radius multiplied by the acceleration due to gravity. Option B is the reciprocal and would make a sharp turn need a smaller bank, which is the opposite of what happens. Option C uses the first power of the speed and so is dimensionally wrong, since the left side is a pure number. Option D multiplies instead of dividing and is wrong on both counts. The same relation explains why the outer rail of a curved railway track is raised and why a cyclist leans inward, and on a level road the safe speed is the square root of the coefficient of friction multiplied by r and g.
Read the full article: Friction and Circular Motion: Laws, Formulas and PYQs
Practice Questions
View allWhen a force resists the relative motion between two surfaces, it is called _______
- A.Resistance
- B.Convection
- C.Friction
- D.Induction
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Friction is defined as the force that opposes the relative motion, or the tendency of relative motion, between two surfaces in contact; it acts along the surfaces and always against the direction of motion.
Read the full explanation →Which of the following statements about the coefficient of friction is correct?
- A.It is measured in newton
- B.It has no unit and no dimensions
- C.It is measured in newton per square metre
- D.It is measured in joule
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The coefficient of friction is the ratio of the limiting or kinetic frictional force to the normal reaction, and since both are forces the ratio is a pure number; the same reasoning applies to other ratios such as the refractive index and relative density.
Read the full explanation →For the same pair of surfaces, which of the following types of friction is the smallest?
- A.Static friction
- B.Limiting friction
- C.Sliding friction
- D.Rolling friction
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When a body rolls, the surfaces in contact change continuously and the irregularities have no time to interlock deeply, so rolling friction is very much smaller than sliding friction; this single fact is the reason the wheel was invented and the reason a ball bearing is fitted wherever a shaft…
Read the full explanation →In uniform circular motion, which of the following quantities remains constant?
- A.Velocity
- B.Speed
- C.Acceleration
- D.Linear momentum
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In uniform circular motion the body covers equal arcs in equal times, so its speed, a scalar, does not change; its kinetic energy and its angular velocity are constant too.
Read the full explanation →A body of mass 5 kg is rotating with angular velocity 10 rad/s in a circular path of radius 0.1 m. Determine the centrifugal force acting on the body.
- A.100 N
- B.50 N
- C.80 N
- D.60 N
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The centrifugal force has the same magnitude as the centripetal force, which for a body moving in a circle is the mass multiplied by the square of the angular velocity multiplied by the radius.
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