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### MATHEMATICS 9709

#### Cambridge International AS and A Level

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

Qtn No. 1 2 3 4 5 6 7 8 9 10 11 12 Total
Marks 6 3 7 8 8 7 6 8 8 8 9 10 88
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 12 questions Question 1 Code: 9709/53/O/N/12/1, Topic: - A circular object is formed from a uniform semicircular lamina of weight$12 \mathrm{~N}$and a uniform semicircular arc of weight$8 \mathrm{~N}$. The lamina and the arc both have centre$O$and radius$0.6 \mathrm{~m}$and are joined at the ends of their common diameter$A B$. The object is freely pivoted to a fixed point at$A$with$A B$inclined at$30^{\circ}$to the vertical. The object is in equilibrium acted on by a horizontal force of magnitude$F \mathrm{~N}$applied at the lowest point of the object, and acting in the plane of the object (see diagram).$\text{(i)}$Show that the centre of mass of the object is at$O$.$\text{(ii)}$Calculate$F$.$$Question 2 Code: 9709/53/O/N/16/1, Topic: - 51 Question 3 Code: 9709/53/O/N/10/2, Topic: - A particle$P$is projected with speed$26 \mathrm{~m} \mathrm{~s}^{-1}$at an angle of$30^{\circ}$above the horizontal from a point$O$on a horizontal plane.$\text{(i)}$For the instant when the vertical component of the velocity of$P$is$5 \mathrm{~m} \mathrm{~s}^{-1}$downwards, find the direction of motion of$P$and the height of$P$above the plane.$\text{(ii)}P$strikes the plane at the point$A$. Calculate the time taken by$P$to travel from$O$to$A$and the distance$O A$.$$Question 4 Code: 9709/53/O/N/12/2, Topic: - A light elastic string has natural length$4 \mathrm{~m}$and modulus of elasticity$60 \mathrm{~N}$. A particle$P$of mass$0.6 \mathrm{~kg}$is attached to the mid-point of the string. The ends of the string are attached to fixed points$A$and$B$which lie in the same vertical line with$A$at a distance of$6 \mathrm{~m}$above$B. P$is projected vertically upwards from the point$2 \mathrm{~m}$vertically above$B$. In the subsequent motion,$P$comes to instantaneous rest at a distance of$2 \mathrm{~m}$below$A$.$\text{(i)}$Calculate the speed of projection of$P$.$\text{(ii)}$Calculate the distance of$P$from$A$at an instant when$P$has its greatest kinetic energy, and calculate this kinetic energy.$$Question 5 Code: 9709/53/O/N/12/3, Topic: - The point$O$is$1.2 \mathrm{~m}$below rough horizontal ground$A B C$. A ball is projected from$O$with speed$25 \mathrm{~ms}^{-1}$at an angle of$70^{\circ}$to the horizontal. The ball passes over the point$A$after travelling a horizontal distance of$2 \mathrm{~m}$. The ball subsequently bounces once on the ground at$B$. The ball leaves$B$with speed$15 \mathrm{~m} \mathrm{~s}^{-1}$and travels a further horizontal distance of$20 \mathrm{~m}$before landing at$C$(see diagram).$\text{(i)}$Calculate the height above the level of$O$of the ball when it is vertically above$A$.$\text{(ii)}$Calculate the time after the instant of projection when the ball reaches$B$.$\text{(iii)}$Find the angle which the trajectory of the ball makes with the horizontal immediately after it bounces at$B$.$$Question 6 Code: 9709/53/O/N/17/3, Topic: - Question 7 Code: 9709/53/O/N/19/3, Topic: - Question 8 Code: 9709/53/O/N/10/4, Topic: - A uniform rod$A B$has weight$15 \mathrm{~N}$and length$1.2 \mathrm{~m}$. The end$A$of the rod is in contact with a rough plane inclined at$30^{\circ}$to the horizontal, and the rod is perpendicular to the plane. The rod is held in equilibrium in this position by means of a horizontal force applied at$B$, acting in the vertical plane containing the rod (see diagram).$\text{(i)}$Show that the magnitude of the force applied at$B$is$4.33 \mathrm{~N}$, correct to 3 significant figures.$\text{(ii)}$Find the magnitude of the frictional force exerted by the plane on the rod.$\text{(iii)}$Given that the rod is in limiting equilibrium, calculate the coefficient of friction between the rod and the plane.$$Question 9 Code: 9709/53/O/N/13/4, Topic: - A particle$P$of mass$0.2 \mathrm{~kg}$is projected horizontally with velocity$0.9 \mathrm{~m} \mathrm{~s}^{-1}$from a point$O$on a rough horizontal surface.$P$moves in a straight line, and at time$t \mathrm{~s}$after projection the velocity of$P$is$v \mathrm{~m} \mathrm{~s}^{-1}$. A force of magnitude$0.024 t \mathrm{~N}$acts on$P$in the direction$O P.$The coefficient of friction between$P$and the surface is$0.3$.$\text{(i)}$Express the acceleration of$P$in terms of$t$, and hence show that, before$P$comes to rest,$$$$v=0.06\left(t^{2}-50 t+15\right)$$$\text{(ii)}$Find the value of$t$when$P$comes to rest.$\text{(iii)}$Find the value of$t$when$P$subsequently begins to move again.$$Question 10 Code: 9709/53/O/N/13/6, Topic: - One end of a light elastic string of natural length$0.8 \mathrm{~m}$and modulus of elasticity$50 \mathrm{~N}$is attached to a fixed point$O$. A particle$P$of mass$0.4 \mathrm{~kg}$is attached to the other end of the string.$P$is projected downwards with speed$1.5 \mathrm{~m} \mathrm{~s}^{-1}$from a point$0.82 \mathrm{~m}$vertically below$O$.$\text{(i)}$Find the greatest speed of$P$.$\text{(ii)}$Show that$P$cannot reach$O$.$\$

Question 11 Code: 9709/53/O/N/19/6, Topic: -

Question 12 Code: 9709/53/O/N/16/7, Topic: -

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