May/June 2026 Paper 41

2026 · 10 questions · 45 parts · 100 marks

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1(a)1(b)(i)1(b)(ii)1(b)(iii)1(b)(iv)

–/10 mks

2(a)2(b)(i)2(b)(ii)2(c)2(d)(i)2(d)(ii)2(d)(iii)

–/13 mks

3(a)3(b)(i)3(b)(ii)3(c)

–/10 mks

4(a)(i)4(a)(ii)4(b)(i)4(b)(ii)

–/9 mks

5(a)5(b)5(c)

–/8 mks

6(a)6(b)(i)6(b)(ii)6(c)(i)6(c)(ii)6(d)

–/12 mks

7(a)(i)7(a)(ii)7(b)

–/8 mks

8(a)8(b)(i)8(b)(ii)8(b)(iii)8(b)(iv)8(c)

–/13 mks

9(a)9(b)(i)9(b)(ii)

–/9 mks

Q10

10(a)10(b)(i)10(b)(ii)10(b)(iii)

–/8 mks

1(a)Gravitational Fields OrbitsEasy2 marks

Define gravitational potential at a point.

Answer

0 words

1(b)(i)Gravitational Fields OrbitsMedium2 marks

A uniform spherical planet has radius

R

. The gravitational potential at its surface is

- Φ

. P is a point on a line that passes through the centre of the planet, at variable displacement

x

from the centre, as shown in Figure 1.1.

Figure 1.1, a spherical planet of radius $R$ with point P on a line through its centre at variable displacement $x$ from the centre

Figure 1.2 shows the variation with

x

of the gravitational potential

ϕ

due to the planet in the region outside the planet close to its surface.

Figure 1.2, a graph of gravitational potential $\phi$ against displacement $x$ outside a planet: two symmetric curves, each passing through $-\Phi$ at $x=\pm R$, through about $-\frac{1}{2}\Phi$ near $x=\pm 2R$, and levelling off towards zero by $x=\pm 3R$

Explain why

ϕ

is negative for all values of

x

Answer

0 words

1(b)(ii)Gravitational Fields OrbitsEasy2 marks

State an expression, in terms of

Φ

and

R

, for the mass

M

of the planet. Identify any other symbols that you use.

Identify

G

1(b)(iii)Gravitational Fields OrbitsEasy1 mark

Determine an expression, in terms of

Φ

and

R

, for the gravitational field strength

g_{0}

at the surface of the planet.

1(b)(iv)Gravitational Fields OrbitsMedium3 marks

On Figure 1.3, sketch the variation of the gravitational field

g

with

x

between

x = - 3 R

and

x = 3 R

. Do not include the region inside the sphere between

x = - R

and

x = R

Draw with the mouse or a finger.