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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

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 $O$. $[3]$

$\text{(ii)}$ Calculate $F$. $[3]$

Question 2 Code: 9709/53/O/N/16/1, Topic: -


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. $[4]$

$\text{(ii)}$ $P$ strikes the plane at the point $A$. Calculate the time taken by $P$ to travel from $O$ to $A$ and the distance $O A$. $[3]$

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 $P$. $[2]$

$\text{(ii)}$ Calculate the distance of $P$ from $A$ at an instant when $P$ has its greatest kinetic energy, and calculate this kinetic energy. $[6]$

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 $A$. $[3]$

$\text{(ii)}$ Calculate the time after the instant of projection when the ball reaches $B$. $[3]$

$\text{(iii)}$ Find the angle which the trajectory of the ball makes with the horizontal immediately after it bounces at $B$. $[2]$

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. $[3]$

$\text{(ii)}$ Find the magnitude of the frictional force exerted by the plane on the rod. $[2]$

$\text{(iii)}$ Given that the rod is in limiting equilibrium, calculate the coefficient of friction between the rod and the plane. $[3]$

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, $[4]$

$$ v=0.06\left(t^{2}-50 t+15\right) $$

$\text{(ii)}$ Find the value of $t$ when $P$ comes to rest. $[2]$

$\text{(iii)}$ Find the value of $t$ when $P$ subsequently begins to move again. $[2]$

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 $P$. $[5]$

$\text{(ii)}$ Show that $P$ cannot reach $O$. $[3]$

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

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

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