June 2023 Paper 1 Q4

OCR MEICurrent spec4 marksMoments

4 A ruler PQRS is a uniform rectangular lamina with mass 20 grams. The length of PQ is 30 cm and the length of PS is 4 cm. The ruler is attached at P to a smooth hinge and held with S vertically below P by a horizontal force of magnitude \(F\) N as shown in the diagram.

Rectangle PQRS with PQ horizontal at the top, hinge at P, S vertically below P, horizontal force F N acting at S

(a) Calculate the value of \(F\). [3]

(b) Explain what would happen to the lamina if the force at S were removed. [1]

Mark scheme (a)

Scheme	Marks	AO
Weight acts through the centre of the ruler 15cm from P	B1	1.1a
Take moments about P \(0.02g \times 15 = F \times 4\)	M1	3.1b
\(F = \dfrac{0.02g \times 15}{4}\) \(= \frac{3g}{40} = 0.735\)	A1	1.1b
	[3]

Notes

B1: Uses uniformity of the ruler, by distance shown on diagram or 15 used in a calculation or equation

M1: Taking moments about any suitable point with all relevant forces and distances attempted. Must include a weight (not mass only) term. Allow one incorrect distance used. Allow 20g for weight or error in converting mass to kilograms or lengths to another unit.

A1: Allow \(0.075g\)

Mark scheme (b)

Scheme	Marks	AO
Without \(F\) the ruler would rotate clockwise [about P]	E1	2.4
	[1]

Notes

E1: Must indicate the turning effect of the weight and the direction. “Clockwise” implies rotation.