A uniform beam of length 60cm weighs 10N. Its centre of gravity (the point where its weight can be assumed to act) is at its centre. A weight of 800N rests at one end of the beam as shown, and the beam is balanced by another weight of 200N placed at distance x from the pivot. What is distance x in cm?

Answer:

10) 39 cm

The problem requires the knowledge of Moments.

Length of beam = 60cm
The weight always acts on the centre of an object. In this case, the centre is (60 ÷ 2) = 30cm.
Weight of beam = 10N

Distance of pivot from centre = 30 – 10 = 20cm

Since the beam is in equilibrium, Clockwise moment = Anti-clockwise moment

Clockwise moment = 10 x 800 = 8000 Ncm

Anti-clockwise moment = (Xcm * 200N) + (10N x 20cm) = 200X + 200 Ncm

8000 = 200X + 200
7800 = 200X
X = 7800 ÷ 200 = 39cm