Mathematics · May / June 2022 · Paper 51 · Question 5
YMA01
As printed in the paper
The question as text
5. 1 m 2 m C D A B 5 m Figure 2 A uniform rod AB has length 5 m and mass 5 kg. The rod rests in equilibrium in a horizontal position on two supports C and D, where AC = 1 m and DB = 2 m , as shown in Figure 2. A particle of mass 10 kg is placed on the rod at A and a particle of mass M kg is placed on the rod at B. The rod remains horizontal and in equilibrium.
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5(a)[3]
C
=
16.25
−
oe or
=
159
−
9.8
or 160
−
9.8
R
g
Mg
R
M
M
C
C
Other possible equations that could be used in (a), to obtain an equation
in
R and M only, or in (b), to obtain an equation in
R and M only
C
D
( ),
R
+
R
=
10
g
+
5
g
+
Mg
C
D
M( ),
A
R
+
3
R
=
5
g
×
2.5
+
5
Mg
C
D
M( ), 4
+
2
=
5
×
2.5
+ ×
5 10
B
R
R
g
g
C
D
M( ), 1.5
+
2.5
=
0.5
+
2.5 10
×
G
R
Mg
R
g
C
D
M( ), 2
×
+ ×
1 10
=
1.5 5
×
+ ×
4
5(b)[3]
C
R
g
g
Mg
D
=
2
−
1.25
oe or
=
19.6
−
12.3 or 20
−
12
R
Mg
g
R
M
M
D
D
Use of when
≥
0 or
≥
0
Allow equality or > 0
R
R
C
D
5(c)[3]
N.B. They may take moments about D or C again, with respectively
R
=
0 or
R
=
0
C
D
M ≤ 16.25 OR M ≥ 0.625 Allow equality
N.B. Allow 2SF or better.
0.625
≤
≤
16.25
M
N.B. Allow 2SF or better.
If either critical value appears, without working or from working done in
parts (a) and/or (b), they can score M1A1ft and also potentially, the
final A1.
Notes for question 5
N.B. Only penalise over accuracy, after use of g = 9.8, ONCE in this
question.
M1 Complete method to give an equation in
R and M only, correct
C
5(a)
number of terms, condone sign errors, dim correct
M0 if they assume that the reactions are equal.
A1 Correct equation(s)
A1 Correct expression (g’s must be collected)
M1 Complete method to give an equation in
R and M only, correct
D
5(b)
number of terms, condone sign errors, dim correct
M0 if they assume that the reactions are equal.
A1 Correct equation(s)
A1 Correct expression (g’s must be collected)
5(c)
M1 Use of either of their reactions to find one critical value
A1ft Critical value of
R OR Critical value of
R
C
D
but must be POSITIVE.
A1 cao Allow 0.625kg
≤
M
kg
≤
16.25kg
(5
−
8 )
= −+
(
4 )
+
3
a
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