# Q. A metallic sphere of mass 1 kG and radius 5cm is welded to the end B of a thin rod AB of length 50 cm and mass 0.5 kG as shown above.This rod with the sphere will balance horizontally on a knife edge placed at a distance 'x' from the end A of the rod if 'x' is equal toA) 35cm   B) 50cm   C) 45cm   D) 55cmI know the answer is 45cm but why didn’t we consider the first particle x co-ordinate to be zero?????

Arun
25757 Points
6 years ago
This system can be imagined to be made of two point masses of 0.5 kg and 1 kg located at the middle (centre of mass) of the original rod and the centre (centre of mass) of the sphere respectively. The distance between these point masses is 30 cm (half the length of rod + radius of the sphere).
The centre of mass of the system is at a distance ‘d’ from the 0.5 kg mass of the rod such that 0.5×d = (30–d)×1.
This gives d = 20 cm. The distance ‘x’ of this centre of mass from the end of the rod is given by x = 25+d = 25+20 = 45 cm.
Therefore, the knife edge is to be placed at 45 cm from the end  [Option (c)].