Which statement defines force?

Question 4

Which statement defines force?

A When a force acts on a body that is free to move, the force is the product of the mass of the body and its acceleration.

B When a force acts on a body that is free to move, the force is the rate of change of

momentum of the body.

C When a force acts on a body that is free to move, the force is the work done by the force divided by the distance moved by the body.

D When a force acts on a lever and causes a moment, the force is the moment divided by the perpendicular distance of the force from the pivot.

Reference: Past Exam Paper – March 2016 Paper 12 Q9

Solution:

Answer: B. 

Force is DEFINED from Newton’s second law of motion. This tells us that the force is proportional to the rate of change of momentum of a body.

F = Δp / Δt = Δ(mv) / Δt

The formula ‘F = ma’ is only a consequence of the second law if we assume that the mass is constant.

F = m(Δv/ Δt) = ma

Choices C and D only deal equations that contain ‘force’. These do not defined force.

A 23892U nucleus decays in two stages to a 23491Pa nucleus. What was emitted in these two stages?

Question 4

A ²³⁸₉₂U nucleus decays in two stages to a ²³⁴₉₁Pa nucleus.

What was emitted in these two stages?

A α + β          B α + γ          C β + β          D β + γ

Reference: Past Exam Paper – November 2008 Paper 1 Q40

Solution:

Answer: A.

During the decay: ²³⁸₉₂U        - - >     …        - - >  ²³⁴₉₁Pa + ???

For any decay, the proton number and mass number must be conserved.

Proton number: 92 = 91 + x

Mass number: 238 = 234 + y

Thus, x = 92 – 91 = 1              and y = 238 – 234 = 4

3 types of radiation can be emitted during radioactive decay: alpha, beta (minus) and gamma. We know that alpha particle is ⁴₂α and beta particle is ⁰_-1β. Gamma is an EM wave and does not have a mass or proton number.

We need to identify which of the combinations provided in the multiple choice would give an overall proton number of +1 and overall mass number of 4.

Consider choice A:     [α and β]

Proton number = 2 + –1 = +1

Mass number = 4 + 0 = 4

So, A is correct

The luminosity L of a star is given by L = 4πr2σT4 where r is the radius of the star

Question 5

The luminosity L of a star is given by

L = 4πr²σT⁴

where

r is the radius of the star,

T is the temperature of the star,

σ is a constant with units W m^-2 K^-4.

What are the SI base units of L?

A kg m² s^-1                        B kg m² s^-2                        C kg m² s^-3                       D kg m² s^-4

Reference: Past Exam Paper – June 2016 Paper 12 Q2

Solution:

Answer: C.

L = 4πr²σT⁴

[L] = [r²] [σ] [T⁴]

4π is a constant that has no unit. {Note that some constants may have units.}

[L] = (m²) (W m^-2 K^-4) (K⁴) = W

The unit W (watt) is not an SI base unit.

Watt is the unit of power.

Power = Work done / time = (Force × distance) / t = (ma × s) / t

Power = (ma × s) / t

[L] = W = (kg) (m s^-2) (m) / s = kg m² s^-3