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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 Total
Marks 11 11 10 11 10 53
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 5 questions Question 1 Code: 9709/51/M/J/16/7, Topic: - A particle$P$is attached to one end of a light elastic string of natural length$1.2 \mathrm{~m}$and modulus of elasticity$12 \mathrm{~N}$. The other end of the string is attached to a fixed point$O$on a smooth plane inclined at an angle of$30^{\circ}$to the horizontal.$P$rests in equilibrium on the plane,$1.6 \mathrm{~m}$from$O$.$\text{(i)}$Calculate the mass of$P$.$$A particle$Q$, with mass equal to the mass of$P$, is projected up the plane along a line of greatest slope. When$Q$strikes$P$the two particles coalesce. The combined particle remains attached to the string and moves up the plane, coming to instantaneous rest after moving$0.2 \mathrm{~m}$.$\text{(ii)}$Show that the initial kinetic energy of the combined particle is$1 \mathrm{~J}$.$$The combined particle subsequently moves down the plane.$\text{(iii)}$Calculate the greatest speed of the combined particle in the subsequent motion.$$Question 2 Code: 9709/53/M/J/16/7, Topic: - 1 51 Question Question 3 Code: 9709/51/O/N/16/7, Topic: - A particle$P$is projected with speed$35 \mathrm{~ms}^{-1}$from a point$O$on a horizontal plane. In the subsequent motion, the horizontal and vertically upwards displacements of$P$from$O$are$x \mathrm{~m}$and$y \mathrm{~m}$respectively. The equation of the trajectory of$P$is $$y=k x-\frac{\left(1+k^{2}\right) x^{2}}{245}$$ where$k$is a constant.$P$passes through the points$A(14, a)$and$B(42,2 a)$, where$a$is a constant.$\text{(i)}$Calculate the two possible values of$k$and hence show that the larger of the two possible angles of projection is$63.435^{\circ}$, correct to 3 decimal places.$$For the larger angle of projection, calculate$\text{(ii)}$the time after projection when$P$passes through$A$,$\text{(iii)}$the speed and direction of motion of$P$when it passes through$B$.$$Question 4 Code: 9709/52/O/N/16/7, Topic: - A small ball$B$of mass$0.5 \mathrm{~kg}$moves in a horizontal circle with centre$O$and radius$0.4 \mathrm{~m}$on the smooth inner surface of a hollow cone fixed with its vertex down. The axis of the cone is vertical and the semi-vertical angle is$60^{\circ}$(see diagram).$\text{(i)}$Show that the magnitude of the force exerted by the cone on$B$is$5.77 \mathrm{~N}$, correct to 3 significant figures, and calculate the angular speed of$B$.$$One end of a light elastic string of natural length$0.45 \mathrm{~m}$and modulus of elasticity$36 \mathrm{~N}$is attached to$B$. The other end of the string is attached to the point on the axis$0.3 \mathrm{~m}$above$O$. The ball$B$again moves on the surface of the cone in the same horizontal circle as before.$\text{(ii)}$Calculate the speed of$B$.$\$

Question 5 Code: 9709/53/O/N/16/7, Topic: -

Worked solutions: P1, P3 & P6 (S1)

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