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### HENRYTAIGO

#### Cambridge International AS and A Level

 Name of student HENRYTAIGO Date Adm. number Year/grade HenryTaigo Stream HenryTaigo Subject Mechanics 2 (M2) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 6 8 6 8 8 6 42
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/51/M/J/11/3, Topic: - A light elastic string of natural length$1.2 \mathrm{~m}$and modulus of elasticity$24 \mathrm{~N}$is attached to fixed points$A$and$B$on a smooth horizontal surface, where$A B=1.2 \mathrm{~m}$. A particle$P$is attached to the mid-point of the string.$P$is projected with speed$0.5 \mathrm{~m} \mathrm{~s}^{-1}$along the surface in a direction perpendicular to$A B$(see diagram).$P$comes to instantaneous rest at a distance$0.25 \mathrm{~m}$from$A B$.$\text{(i)}$Show that the mass of$P$is$0.8 \mathrm{~kg}$.$[3]\text{(ii)}$Calculate the greatest deceleration of$P$.$[3]$Question 2 Code: 9709/52/M/J/11/3, Topic: - A particle$P$of mass$0.5 \mathrm{~kg}$is attached to the vertex$V$of a fixed solid cone by a light inextensible string.$P$lies on the smooth curved surface of the cone and moves in a horizontal circle of radius$0.1 \mathrm{~m}$with centre on the axis of the cone. The cone has semi-vertical angle$60^{\circ}$(see diagram).$\text{(i)}$Calculate the speed of$P$, given that the tension in the string and the contact force between the cone and$P$have the same magnitude.$[4]\text{(ii)}$Calculate the greatest angular speed at which$P$can move on the surface of the cone.$[4]$Question 3 Code: 9709/53/M/J/11/3, Topic: - A smooth hemispherical shell, with centre$O$, weight$12 \mathrm{~N}$and radius$0.4 \mathrm{~m}$, rests on a horizontal plane. A particle of weight$W \mathrm{~N}$lies at rest on the inner surface of the hemisphere vertically below$O$. A force of magnitude$F \mathrm{~N}$acting vertically upwards is applied to the highest point of the hemisphere, which is in equilibrium with its axis of symmetry inclined at$20^{\circ}$to the horizontal (see diagram).$\text{(i)}$Show, by taking moments about$O$, that$F=16.48$correct to 4 significant figures.$[3]\text{(ii)}$Find the normal contact force exerted by the plane on the hemisphere in terms of$W$. Hence find the least possible value of$W$.$[3]$Question 4 Code: 9709/51/O/N/11/3, Topic: - One end of a light elastic string of natural length$0.4 \mathrm{~m}$and modulus of elasticity$20 \mathrm{~N}$is attached to a fixed point$O$. The other end of the string is attached to a particle$P$of mass$0.25 \mathrm{~kg}. P$hangs in equilibrium below$O$.$\text{(i)}$Calculate the distance$O P$.$[2]$The particle$P$is raised, and is released from rest at$O$.$\text{(ii)}$Calculate the speed of$P$when it passes through the equilibrium position.$[3]\text{(iii)}$Calculate the greatest value of the distance$O P$in the subsequent motion.$[3]$Question 5 Code: 9709/52/O/N/11/3, Topic: - Question 6 Code: 9709/53/O/N/11/3, Topic: - A particle$P$is projected with speed$25 \mathrm{~m} \mathrm{~s}^{-1}$at an angle of$45^{\circ}$above the horizontal from a point$O$on horizontal ground. At time$t \mathrm{~s}$after projection the horizontal and vertically upward displacements of$P$from$O$are$x \mathrm{~m}$and$y \mathrm{~m}$respectively.$\text{(i)}$Express$x$and$y$in terms of$t$and hence show that the equation of the path of$P$is$y=x-0.016 x^{2}$.$[4]\text{(ii)}$Calculate the horizontal distance between the two positions at which$P$is$2.4 \mathrm{~m}$above the ground.$[2]\$

Worked solutions: P1, P3 & P6 (S1)

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