Which one of the following physical quantities has the same dimensions as that of Planck's constant h?
- A.Linear momentum
- B.Angular momentum
- C.Force
- D.Potential energy
Correct answer
Explanation
The correct answer is B, Angular momentum. Planck's constant has the same dimensions as angular momentum, [M L² T⁻¹].
Planck's constant links the energy of a photon to its frequency through E = hν, so h = E/ν. Energy has dimensions [M L² T⁻²] and frequency has [T⁻¹], which gives h the dimensions [M L² T⁻¹] and the SI unit joule-second. Angular momentum is moment of inertia times angular velocity, or r × p, which also works out to [M L² T⁻¹] with the unit kg m² s⁻¹, the same as J s. This is why Bohr could state that the angular momentum of an electron in an allowed orbit is a whole multiple of h/2π.
A is wrong because linear momentum has dimensions [M L T⁻¹]. C is wrong because force has dimensions [M L T⁻²]. D is wrong because potential energy has dimensions [M L² T⁻²], which is energy, not energy multiplied by time.
Exam tip: h = E/ν = joule-second = [M L² T⁻¹], the same as angular momentum.
Practice Questions
View allWhich one of the following is not true for anodizing process?
- A.It makes aluminium corrosion resistant.
- B.Metals like aluminium, titanium and magnesium can be anodized.
- C.Clean aluminium article is the anode and oxygen gas is evolved at the cathode.
- D.It is used in aircraft industry.
Show answer
In anodizing the clean aluminium article is indeed the anode, but oxygen is released at the anode, not at the cathode; hydrogen is released at the cathode.
Read the full explanation →Which one of the following statements is not correct?
- A.The response of the ear to sound of increasing intensity is approximately logarithmic.
- B.The sensitivity of the human ear does not vary with the frequency of the sound.
- C.When two or more waves traverse the same medium, the displacement of any element of the medium is the algebraic sum of the displacements due to each wave.
- D.Longitudinal waves can travel in all media—solids, liquids and gases.
Show answer
The statement that the sensitivity of the human ear does not vary with frequency is false, because the ear is far more sensitive to some frequencies than to others.
Read the full explanation →Kwashiorkor disease in children is caused by
- A.sufficient carbohydrates but less fats in diet
- B.sufficient carbohydrates and fats but deficient proteins in diet
- C.sufficient vitamins but deficient fats in diet
- D.sufficient fats but deficient vitamins in diet
Show answer
Kwashiorkor is a disease of protein deficiency in a child who still gets enough calories. It usually appears when a child is weaned from breast milk onto a starchy diet with little protein.
Read the full explanation →Which one of the following is the correct order of pH for the given substances?
- A.Coffee < Lemon juice < Milk of magnesia < Blood
- B.Milk of magnesia < Blood < Coffee < Lemon juice
- C.Lemon juice < Blood < Coffee < Milk of magnesia
- D.Lemon juice < Coffee < Blood < Milk of magnesia
Show answer
Arranged from most acidic to most basic, the four substances fall in exactly this order. Lemon juice, rich in citric acid, has a pH of about 2 to 2.5.
Read the full explanation →Which one of the following diseases may be caused by the deficiency of vitamin C?
- A.Rickets
- B.Rabies
- C.Hepatitis
- D.Scurvy
Show answer
Scurvy is caused by a lack of vitamin C, or ascorbic acid, which the body needs to make collagen, the protein that holds skin, gums and blood vessels together.
Read the full explanation →