(i)[3]
Show that the horizontal distance of the centre of mass of the wire from the wall is $0.463\,\text{m}$, correct to $3$ significant figures.
(ii)[2]
Calculate the wire's weight.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A uniform wire is shaped into a semicircular arc, and its diameter AB has a length of $0.8\,\text{m}$. It is fixed to a vertical wall by a smooth hinge at $A$. The wire is in equilibrium, with $AB$ inclined at $70^\circ$ to the upward vertical, and it is supported by a light string attached at $B$. The other end of the string is fastened to the point $C$ on the wall, $0.8\,\text{m}$ vertically above $A$. The tension in the string is $15\,\text{N}$ (see diagram).