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### RONALDWREWS

#### Cambridge International AS and A Level

 Name of student RONALDWREWS Date Adm. number Year/grade 1982 Stream Ronaldwrews Subject Mechanics 2 (M2) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 6 6 8 7 8 35
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 5 questions Question 1 Code: 9709/51/M/J/10/3, Topic: - A particle of mass$0.24 \mathrm{~kg}$is attached to one end of a light inextensible string of length$2 \mathrm{~m}$. The other end of the string is attached to a fixed point. The particle moves with constant speed in a horizontal circle. The string makes an angle$\theta$with the vertical (see diagram), and the tension in the string is$T \mathrm{~N}$. The acceleration of the particle has magnitude$7.5 \mathrm{~m} \mathrm{~s}^{-2}$.$\text{(i)}$Show that$\tan \theta=0.75$and find the value of$T$.$\text{(ii)}$Find the speed of the particle.$$Question 2 Code: 9709/52/M/J/10/3, Topic: - Question 3 Code: 9709/53/M/J/10/3, Topic: - Two particles$P$and$Q$are projected simultaneously with speed$40 \mathrm{~m} \mathrm{~s}^{-1}$from a point$O$on a horizontal plane. Both particles subsequently pass at different times through the point$A$which has horizontal and vertically upward displacements from$O$of$40 \mathrm{~m}$and$15 \mathrm{~m}$respectively.$\text{(i)}$By considering the equation of the trajectory of a projectile, show that each angle of projection satisfies the equation$\tan ^{2} \theta-8 \tan \theta+4=0$.$\text{(ii)}$Calculate the distance between the points at which$P$and$Q$strike the plane.$$Question 4 Code: 9709/52/O/N/10/3, Topic: - Question 5 Code: 9709/53/O/N/10/3, Topic: - Particles$P$and$Q$have masses$0.8 \mathrm{~kg}$and$0.4 \mathrm{~kg}$respectively.$P$is attached to a fixed point$A$by a light inextensible string which is inclined at an angle$\alpha^{\circ}$to the vertical.$Q$is attached to a fixed point$B$, which is vertically below$A$, by a light inextensible string of length$0.3 \mathrm{~m}$. The string$B Q$is horizontal.$P$and$Q$are joined to each other by a light inextensible string which is vertical. The particles rotate in horizontal circles of radius$0.3 \mathrm{~m}$about the axis through$A$and$B$with constant angular speed$5 \mathrm{rad} \mathrm{s}^{-1}$(see diagram).$\text{(i)}$By considering the motion of$Q$, find the tensions in the strings$P Q$and$B Q$.$\text{(ii)}$Find the tension in the string$A P$and the value of$\alpha$.$\$

Worked solutions: P1, P3 & P6 (S1)

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