PHY1505
Assignment 4
2025
, Assignment 04 (2025)
Total mark: 100
Mechanics
Department of Physics
Question 1 (5 marks)
Problem: Shrink Earth to fraction 𝑓 of its current radius (mass unchanged). For what 𝑓
would surface gravity be three times current 𝑔?
𝐺𝑀
Workings Surface gravity 𝑔 = . If new radius 𝑅 ′ = 𝑓𝑅, then
𝑅2
𝐺𝑀 𝑔
𝑔′ = = .
(𝑓𝑅) 2 𝑓 2
Require 𝑔′ = 3𝑔:
𝑔 1 1
= 3𝑔 ⇒ =3 ⇒ 𝑓= .
𝑓2 𝑓2 √3
Answer
1
𝑓= ≈ 0.577 (i.e. 57.7% of current radius).
√3
Question 2 (6 marks)
Problem: Two identical stars (each 𝑀 = 1.99 × 10 30 kg) separated by 𝐷 =
8.0 × 1011 km = 8.0 × 10 14 m. Comet starts at rest from infinity and falls along the line
through the midpoint. Speed at midpoint?
Workings
Distance from midpoint to each star:
𝐷
𝑟= = 4.0 × 10 14 m.
2
Assignment 4
2025
, Assignment 04 (2025)
Total mark: 100
Mechanics
Department of Physics
Question 1 (5 marks)
Problem: Shrink Earth to fraction 𝑓 of its current radius (mass unchanged). For what 𝑓
would surface gravity be three times current 𝑔?
𝐺𝑀
Workings Surface gravity 𝑔 = . If new radius 𝑅 ′ = 𝑓𝑅, then
𝑅2
𝐺𝑀 𝑔
𝑔′ = = .
(𝑓𝑅) 2 𝑓 2
Require 𝑔′ = 3𝑔:
𝑔 1 1
= 3𝑔 ⇒ =3 ⇒ 𝑓= .
𝑓2 𝑓2 √3
Answer
1
𝑓= ≈ 0.577 (i.e. 57.7% of current radius).
√3
Question 2 (6 marks)
Problem: Two identical stars (each 𝑀 = 1.99 × 10 30 kg) separated by 𝐷 =
8.0 × 1011 km = 8.0 × 10 14 m. Comet starts at rest from infinity and falls along the line
through the midpoint. Speed at midpoint?
Workings
Distance from midpoint to each star:
𝐷
𝑟= = 4.0 × 10 14 m.
2
