I think it is the same one. See the following snippets.
Motherwell Times 10-9-1909:
Offers were opened for the widening of Wind-
mill Street at Knowetop Quarry, and remit-
ted to the Burgh Surveyor to check and accept
the lowest.
Motherwell Times 2-9-1921:
Speaking about the late "Granny Tamson" -
Her husband, the late Thomas Thomson,
was quarry foreman to the late Mr King,
when Knowetop Quarry was in operation.
Motherwell Times 3-2-1939:
John Park telling the Rotary Club about his boyhood in Motherwell -
Knowetop quarry was an adventurous
hunting ground for youngsters in those days,
not only for the peculiar terrain it pro-
vided, but because of the picturesque work-
men who were employed there, men who
used a forceful and colourful dialect. When
the main road was being constructed part
of the quarry was bridged over to carry the
road: a splendid A.R.P. shelter for anyone
who can find it.
Motherwell Times 14-6-1929 - William Law recalls his youth -
He remembers
when "Homey" King was killed at Knowe-
top Quarry. The latter was a member of
the well-known King family, who have
been intimately concerned in the growth
and expansion of the town. [he describes his elaborate funeral]
Motherwell Times 30-7-1954:
The first treasurer was a
son of Mr James King who
owned Knowetop and other
quarries in the neighbourhood.