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Date	November 2020	Marks available	3	Reference code	20N.3.SL.TZ0.8
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show that	Question number	8	Adapted from	N/A

Question

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 $\sqrt{\frac{10 g h}{7}}$ .

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 ✓

Examiners report

[N/A]

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.1 – Rigid bodies and rotational dynamics

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18M.3.SL.TZ2.6a.ii:
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16N.3.SL.TZ0.8a:
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18N.3.SL.TZ0.6c.i:
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18N.3.SL.TZ0.6b.i:
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17N.3.SL.TZ0.7d:
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17M.3.SL.TZ1.5b.ii:
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18M.3.SL.TZ2.6a.i:
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18M.3.SL.TZ1.6c:
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20N.3.SL.TZ0.6a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
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17N.3.SL.TZ0.7e:
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19N.3.SL.TZ0.5c(ii):
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19M.3.SL.TZ2.9a:
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20N.3.SL.TZ0.6d:
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20N.3.SL.TZ0.6c:
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17M.3.SL.TZ2.6b:
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17N.3.SL.TZ0.7b:
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17M.3.SL.TZ1.5a.i:
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19M.3.SL.TZ2.9b:
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Option B: Engineering physics