DP Physics (first assessment 2025)

Question 20N.2.HL.TZ0.8

Date	November 2020	Marks available	[Maximum mark: 3]	Reference code	20N.2.HL.TZ0.8
Level	HL	Paper	2	Time zone	TZ0
Command term	Show that	Question number	8	Adapted from	N/A

[Maximum mark: 3]

20N.2.HL.TZ0.8

A solid sphere of radius $r$ and mass $m$ is released from rest and rolls down a slope, without slipping. The vertical height of the slope is $h$ . The moment of inertia $I$ of this sphere about an axis through its centre is $\frac{2}{5} m r^{2}$ .

Show that the linear velocity $v$ of the sphere as it leaves the slope is $\sqrt{\frac{10 g h}{7}}$ .

[3]

Markscheme

conservation of rotational and linear energy

OR
$m g h = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$ ✓

using $I = \frac{2}{5} m r^{2}$ AND $ω = \frac{v}{r}$ ✓

with correct manipulation to find the requested relationship ✓

Syllabus sections

A. Space, time and motion » A.4 Rigid body mechanics

Question 20N.2.HL.TZ0.8

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