$\require{\cancel}$ $\require{\stix[upint]}$

Qtn No.	1	2	3	4	5	6	Total
Marks	5	5	7	7	7	8	39
Score

Question 1 Code: 9709/51/M/J/10/4, Topic: -

 

A uniform lamina of weight $15 \mathrm{~N}$ is in the form of a trapezium $A B C D$ with dimensions as shown in the diagram. The lamina is freely hinged at $A$ to a fixed point. One end of a light inextensible string is attached to the lamina at $B$. The lamina is in equilibrium with $A B$ horizontal; the string is taut and in the same vertical plane as the lamina, and makes an angle of $30^{\circ}$ upwards from the horizontal (see diagram). Find the tension in the string. $[5]$

Question 2 Code: 9709/52/M/J/10/4, Topic: -

Question 3 Code: 9709/53/M/J/10/4, Topic: -

 

$A B$ is the diameter of a uniform semicircular lamina which has radius $0.3 \mathrm{~m}$ and mass $0.4 \mathrm{~kg}$. The lamina is hinged to a vertical wall at $A$ with $A B$ inclined at $30^{\circ}$ to the vertical. One end of a light inextensible string is attached to the lamina at $B$ and the other end of the string is attached to the wall vertically above $A$. The lamina is in equilibrium in a vertical plane perpendicular to the wall with the string horizontal (see diagram).

$\text{(i)}$ Show that the tension in the string is $2.00 \mathrm{~N}$ correct to 3 significant figures. $[4]$

$\text{(ii)}$ Find the magnitude and direction of the force exerted on the lamina by the hinge. $[3]$

Question 4 Code: 9709/51/O/N/10/4, Topic: -

 

A uniform beam $A B$ has length $2 \mathrm{~m}$ and weight $70 \mathrm{~N}$. The beam is hinged at $A$ to a fixed point on a vertical wall, and is held in equilibrium by a light inextensible rope. One end of the rope is attached to the wall at a point $1.7 \mathrm{~m}$ vertically above the hinge. The other end of the rope is attached to the beam at a point $0.8 \mathrm{~m}$ from $A$. The rope is at right angles to $A B$. The beam carries a load of weight $220 \mathrm{~N}$ at $B$ (see diagram).

$\text{(i)}$ Find the tension in the rope. $[3]$

$\text{(ii)}$ Find the direction of the force exerted on the beam at $A$. $[4]$

Question 5 Code: 9709/52/O/N/10/4, Topic: -

Question 6 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. $[3]$