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Qtn No.	1	2	3	4	5	6	Total
Marks	8	8	8	9	10	9	52
Score

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: -