Which one of the following is dimensionless quantity?
- A.Stress
- B.Strain
- C.Pressure
- D.Force
Correct answer
Explanation
The correct answer is B, Strain. Strain is a ratio of two lengths (or two volumes), so its units cancel and it has no dimensions.
When a force deforms a body, strain measures the fractional change in its shape or size. Longitudinal strain is the change in length divided by the original length, ΔL/L; volume strain is ΔV/V; and shearing strain is an angle in radians. Since each is one length divided by another, strain has no unit and the dimensional formula [M⁰L⁰T⁰]. By Hooke's law, within the elastic limit stress is proportional to strain, and the ratio stress/strain is the modulus of elasticity, which therefore has the same unit as stress.
A is wrong: stress is force per unit area, measured in N/m² or pascal, with dimensions [ML⁻¹T⁻²]. C is wrong: pressure is also force per unit area and has the same dimensions as stress. D is wrong: force is measured in newtons, with dimensions [MLT⁻²].
Exam tip: strain, refractive index, relative density and angle (radian) are common dimensionless quantities; stress, pressure and Young's modulus share [ML⁻¹T⁻²].
Practice Questions
View allA negative work is done when an applied force F and the corresponding displacement S are
- A.perpendicular to each other.
- B.parallel to each other.
- C.anti-parallel to each other.
- D.equal in magnitude.
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Work is negative when the force acts opposite to the displacement, because the angle between them is then 180°. Work done is W = F S cos θ, where θ is the angle between the force and the displacement.
Read the full explanation →Which one of the following statements about a satellite orbiting around the Earth is correct ?
- A.Satellite is kept in orbit by remote control from ground station.
- B.Satellite is kept in orbit by retro-rocket and solar energy keeps it moving around the Earth.
- C.Satellite requires energy from solar panels and solid fuels for orbiting.
- D.Satellite does not require any energy for orbiting.
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Read the full explanation →Which one of the following is not a conservative force ?
- A.Frictional force
- B.Electric force
- C.Gravitational force
- D.Spring force
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Friction is a non-conservative force because the work it does depends on the path taken and the energy it removes is lost as heat.
Read the full explanation →A microphone converts
- A.electrical signals to sound waves
- B.sound waves to electrical signals
- C.microwaves to sound waves
- D.sound waves to microwaves
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A microphone is a transducer that changes the pressure variations of sound into a matching electrical signal. In a common dynamic microphone, sound waves make a thin diaphragm vibrate.
Read the full explanation →When a light ray passes through from air to water with a non-zero angle the ray will be
- A.bending towards the normal
- B.bending away from the normal
- C.propagating in straight line
- D.reflected towards the opposite direction
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Light slows down when it enters water from air, so a ray that strikes the surface at an angle bends towards the normal.
Read the full explanation →