Mathematics · Oct / Nov 2023 · Paper 51 · Question 5
YMA01
As printed in the paper
The question as text
5. θ Figure 3 A small ring of mass 0.2 kg is attached to one end of a light inextensible string. The ring is threaded onto a fixed rough vertical rod. The string is taut and makes an angle θ with the rod, as shown in Figure 3, 12 where θ tan 5 Given that the ring is in equilibrium and that the tension in the string is 10 N,
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
5(a)[3]
=
10cos
θ
−
0.2
or
=
0.2
−
10cos
θ
F
g
F
g
| F | = 1.9 or1.89 (N)
Friction acts downwards or down.
5(b)[1]
A0 for anything else.
5(c)[8]
R
=
T
sin
θ
12
T
R
=
13
1
F
=
R
4
Resolve vertically
For min value
T
cos
θ=
0.2
g
−
F
For max value
cos
θ=
0.2
+
T
g
F
(i)
Min T 3.2 or 3.19 (N)
Max T 13 or12.7 (N)
(ii)
N.B. Penalise over accuracy once for the whole question and
penalise the FIRST time it is seen.
N.B. If 2 instead of 0.2 is used throughout the WHOLE
question, treat as a MR.
Notes for question 5
Resolve vertically, dimensionally correct, condone sin/cos confusion and sign
(a) M1
errors.
Correct unsimplified equation.
A1
A1
Correct value for Friction, must be positive
N.B. If they use
as their notation for F and never separate μand R, allow
μ
R
M1A1A1. If, however, they do separate them, give M1A1A0.
Correct direction from a correct, but possibly unrounded, answer to part (a).
(b) A1
Resolve perpendicular to the rod. Must be dimensionally correct and have
(c) M1
correct no of terms. Condone sin/cos confusion.
N.B. M0 if they use T = 10
A1
Correct unsimplified equation
B1
1
=
seen or implied
F
R
4
M1
Resolve parallel to the rod for either case. Must be dimensionally correct and
have correct no of terms. Condone sin/cos confusion.
N.B. M0 if they use T = 10 or if they use F from part (a).
A1
Correct minimum case equation
Correct maximum case equation
A1
(i)A1
cao for min T. Allow 0.325g
cao for max T Allow 1.3g
(ii)A1
N.B. If only one found and no labels, allow the A mark for the equation but
must state which one it is to score the A mark for the answer.
N.B. If both correctly found and no labels, allow all the marks.
N.B. If both correctly found but the answers are labelled wrongly, lose the final
two A marks.
(20
+
34 )
−
(15
+
36 )
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