Mathematics · May / June 2024 · Paper 51 · Question 4
YMA01
As printed in the paper
The question as text
4. 6.5 m 1.5 m C B A Figure 2 A non‑uniform rod AB has length 6.5 m and mass 1.2 kg. The centre of mass of the rod is 3 m from A. The rod rests on a horizontal step and overhangs the end of the step C by 1.5 m, as shown in Figure 2. The rod is perpendicular to the edge of the step. A particle of mass 4 kg is placed on the rod at B and another particle, whose mass is M kg, is placed on the rod at D, where AD = 0.5 m. The rod remains in equilibrium in a horizontal position.
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4(a)[3]
M C
Mg
g
g
M = 0.8 oe
Other possible equations:
( ),
Y
=
4
g
+
1.2
g
+
Mg
M A
( ), 5
Y
=
1.2
g
×+
3
4
g
×
6.5
+
Mg
×
0.5
M B
( ), 1.5
Y
=
1.2
g
×
3.5
+
Mg
×
6
M G
( ), 2
Y
+
Mg
×
2.5
=
4
g
×
3.5
from which Y would need to be eliminated.
( ),
×
0.6
=
1.2
×
2.6
4(b)[3]
M E
R
g
C
R
=
5.2
g
isw
C
Other possible equations:
( ),
Xg
+
1.2
g
=
R
C
( ),
×
0.6
=
1.2
×
2
M C
Xg
g
( ), 1.2
×+
3
×
5.6
=
×
5
M A
g
Xg
R
C
( ), 1.2
3.5
0.9
1.5
M B
g
×
+
Xg
×
=
R
×
C
M G
( ),
Xg
×
2.6
=
R
×
2
C
from which Xg would need to be eliminated. (Note that X = 4)
Xg may appear as a single letter.
Notes
M1: For an equation in M only, with correct number of terms, condone
4(a)
sign errors and missing g’s
A1: Correct equation
A1: cao
M1: For an equation in
R only, with correct number of terms, condone
4(b)
C
sign errors and missing g’s
A1: Correct equation
g , 51 or 51.0
A1: 26
5
1
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