Home / IBDP Physics- A.5 Galilean and special relativity- IB Style Questions For HL Paper 1A

IBDP Physics- A.5 Galilean and special relativity- IB Style Questions For HL Paper 1A -FA 2025

IBDP Physics HL Paper 1 -FA 2025- All Chapters

Question 

Rocket R travels away from an observer on Earth at a speed of \(0.80c\). A space-time diagram shows four world lines.

What is the correct world line of R in the reference frame of Earth?

(A) A
(B) B
(C) C
(D) D
▶️ Answer/Explanation

Correct Answer: \( \boxed{\mathrm{B}} \)

For an object moving at speed \(v\), its world line on a \(ct\)-\(x\) space-time diagram satisfies

\(v=\dfrac{x}{t}\)

Since the vertical axis is \(ct\), the gradient of the world line is related to the speed by

\(\dfrac{ct}{x}=\dfrac{c}{v}\)

For rocket R,

\(v=0.80c\)

Therefore,

\(\dfrac{ct}{x}=\dfrac{c}{0.80c}=1.25\)

The correct world line must therefore represent a speed of \(0.80c\), corresponding to line B on the diagram.

Hence, the correct answer is \( \boxed{\mathrm{B}} \).

Question 

The fixed distance between Earth and a star measured in Earth’s reference frame is \(d_{\mathrm{E}}\). A spaceship travels from Earth to the star at a constant speed of \(0.8c\) relative to Earth. The distance between Earth and the star as measured by the spaceship is \(d_{\mathrm{S}}\).

What is \(\dfrac{d_{\mathrm{S}}}{d_{\mathrm{E}}}\)?

(A) \(\dfrac{3}{5}\)
(B) \(\dfrac{4}{5}\)
(C) \(\dfrac{5}{4}\)
(D) \(\dfrac{5}{3}\)
▶️ Answer/Explanation

Correct Answer: \( \boxed{\mathrm{A}} \)

The distance measured in the reference frame in which the two objects are moving is length contracted.

The length contraction equation is

\(d_{\mathrm{S}}=\dfrac{d_{\mathrm{E}}}{\gamma}\)

where the Lorentz factor is

\(\gamma=\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}\)

For \(v=0.8c\),

\(\gamma=\dfrac{1}{\sqrt{1-(0.8)^2}}\)

\(\gamma=\dfrac{1}{\sqrt{1-0.64}}=\dfrac{1}{0.6}=\dfrac{5}{3}\)

Therefore,

\(d_{\mathrm{S}}=\dfrac{d_{\mathrm{E}}}{\dfrac{5}{3}}=\dfrac{3}{5}d_{\mathrm{E}}\)

Hence,

\( \boxed{\dfrac{d_{\mathrm{S}}}{d_{\mathrm{E}}}=\dfrac{3}{5}} \)

Hence, the correct answer is \( \boxed{\mathrm{A}} \).

Question

Choose the speed at which the mass of an electron is double its rest mass.
(A) \(c\)
(B) \( \dfrac{\sqrt{3}}{2}c \)
(C) \( \dfrac{1}{2}c \)
(D) None of these
▶️ Answer/Explanation
Detailed solution

The relativistic mass of a particle moving at speed \(v\) is given by \( m=\dfrac{m_0}{\sqrt{1-\dfrac{v^2}{c^2}}} \), where \(m_0\) is the rest mass.

If the mass of the electron is double its rest mass, then \( m = 2m_0 \).

Hence, \( 2 = \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}} \).

Squaring both sides gives \( 1-\dfrac{v^2}{c^2} = \dfrac{1}{4} \).

Therefore, \( \dfrac{v^2}{c^2} = \dfrac{3}{4} \) and \( v = \dfrac{\sqrt{3}}{2}c \).

✅ Answer: (B)

More A.5 Galilean and special relativity HL Paper 1 Questions..
Scroll to Top