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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 8 8 8 9 10 9 52
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/51/M/J/19/5, Topic: - A particle$P$of mass$0.4 \mathrm{~kg}$is attached to one end of a light elastic string of natural length$0.5 \mathrm{~m}$and modulus of elasticity$6 \mathrm{~N}$. The other end of the string is attached to a fixed point$O$. The particle$P$is released from rest at the point$(0.5+x) \mathrm{m}$vertically below$O$. The particle$P$comes to instantaneous rest at$O$.$\text{(i)}$Find$x$.$[3]\text{(ii)}$Find the greatest speed of$P$.$[5]$Question 2 Code: 9709/52/M/J/19/5, Topic: - A light elastic string has natural length$a \mathrm{~m}$and modulus of elasticity$\lambda \mathrm{N}$. When the length of the string is$1.6 \mathrm{~m}$the tension is$4 \mathrm{~N}$. When the length of the string is$2 \mathrm{~m}$the tension is$6 \mathrm{~N}$.$\text{(i)}$Find the values of$a$and$\lambda$.$[5]$One end of the string is attached to a fixed point$O$on a smooth horizontal surface. The other end of the string is attached to a particle$P$of mass$0.2 \mathrm{~kg}$. The particle$P$moves with constant speed on the surface in a circle with centre$O$and radius$1.9 \mathrm{~m}$.$\text{(ii)}$Find the speed of$P$.$[3]$Question 3 Code: 9709/53/M/J/19/5, Topic: - Question 4 Code: 9709/51/O/N/19/5, Topic: - A particle$P$of mass$0.3 \mathrm{~kg}$is attached to one end of a light elastic string of natural length$0.6 \mathrm{~m}$and modulus of elasticity$9 \mathrm{~N}$. The other end of the string is attached to a fixed point$O$on a smooth plane inclined at$30^{\circ}$to the horizontal.$O A$is a line of greatest slope of the plane with$A$below the level of$O$and$O A=0.8 \mathrm{~m}$. The particle$P$is released from rest at$A$.$\text{(i)}$Find the initial acceleration of$P$.$[4]\text{(ii)}$Find the greatest speed of$P$.$[5]$Question 5 Code: 9709/52/O/N/19/5, Topic: -$A$and$B$are two fixed points on a vertical axis with$A$above$B$. A particle$P$of mass$0.4 \mathrm{~kg}$is attached to$A$by a light inextensible string of length$0.5 \mathrm{~m}$. The particle$P$is attached to$B$by another light inextensible string.$P$moves with constant speed in a horizontal circle with centre$O$between$A$and$B$. Angle$B A P=30^{\circ}$and angle$A B P=70^{\circ}$(see diagram).$\text{(i)}$Given that the tensions in the two strings are equal, find the speed of$P$.$[5]\text{(ii)}$Given instead that the angular speed of$P$is$12 \mathrm{rad} \mathrm{s}^{-1}$, find the tensions in the strings.$[5]\$

Question 6 Code: 9709/53/O/N/19/5, Topic: -

Worked solutions: P1, P3 & P6 (S1)

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