Mathematics · Oct / Nov 2022 · Paper 51 · Question 2
YMA01
As printed in the paper
The question as text
2. 2 3 5 a 5 a A C D B 2a Figure 1 A uniform rod AB has length 2a and mass M. The rod is held in equilibrium in a horizontal position by two vertical light strings which are attached to the rod at C and D, where AC = 2 5 a and DB = 3 5 a, as shown in Figure 1. A particle P is placed on the rod at B. The rod remains horizontal and in equilibrium.
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2(a)[3]
a
a
M( ), 5
D
Xg
=
Mg
5
Other possible equations:
( )
T
=
Mg
+
Xg
D
7
a
M( ),
+
2
=
A
Mga
Xg a
T
D
5
3
a
M( ),
B
Mga
=
T
T would then need to be eliminated
D
5
D
3
8
a
a
M( ),
C
Mg
+
Xg
=
T a
5
5
D
2
a
M( ),
=
G
Xga
T
D
5
2
M
X =
, 0.67 M or better
3
2(b)[3]
1
3
a
2
a
M( ),
+
=
D T a
Mg
Mg
C
2
5
5
Other possible equations:
1
( )
+
=
+
T
T
Mg
Mg
C
D
2
1
2
a
7
a
M( ),
+
2
=
+
A
Mga
Mg a
T
T
2
C
5
D
5
8
3
a
a
M( ),
=
+
T would need eliminating
B
Mga
T
T
C
5
D
5
D
3
1
8
a
a
M( ),
C
Mg
+
Mg
=
T a
5
2
5
D
3
1
2
a
a
M( ),
G
T
+
Mga
=
T
C
5
2
D
5
1
=
oe
T
Mg
C
10
Notes for question 2
M1 For an equation (or inequality,„ ) in X , M and a only (allow
consistent missing a’s) with correct no. of terms.
2(a)
Allow if one g is missing.
N.B. M0 if Tc appears and never becomes zero
A1 Correct equation or inequality
A1 cao
M1 For an equation in Tc , M , g and a only (allow consistent missing
a’s or if g(’s) missing) with correct no. of terms
2(b)
M0 if they assume that
T
=
T
or if they assume their X value from
C
D
(a).
A1 Correct equation
A1 cao
R
F
14.7
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