Solution 2

Solution2:
One of the first definitions of center of gravity that a student learns is that it is the point at which the object can be balanced using a pinhead...
The point of hinging is the center of mass (equivalent to center of gravity here) of the Rod-balls system. The Rod being massless contributes nothing.

COM=∑(Mi*Xi)/∑Mi

The center of mass of the balls are at the positions of the rod where they are placed...at least the x-coordinates are.

→COM=(1.1+2.2+3.3+...+100.100)/(1+2+3+...+100)

=(100*101*201/6)/(100*101/2)....applying sum of 1st n naturals...and of their squares.

→COM=67...which is the point of hinging...

9 comments:

  1. if we are taking one end as the origin then shouldn't it go like this 1*0 + 2*1 ------------ and so on

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  2. ya..there was some problem with the diagram...
    Still the data given specifies 1kg at 1...

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  3. anyways you could solve it, right... i'll be careful next.

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  4. so maybe 66 would be correct if you solved it kartik's way?

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  5. These questions are interesting.
    When is the next one coming??

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  6. thanks bhaiya your corrections made my confidence boost up

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  9. vibhav said...
    kartik, it doesnt make a difference whether u do 1*0 or 1*1. in the former u'll get 66 as the answer and in the latter 67
    both answers are correct
    however, in the latter, ur axis lies BEFORE the first ball, which means 67th ball from d beginning...
    while in the former, ur axis passes THROUGH the first ball, and 66 represents distance FROM the first ball, which would again imply 67th ball from d beginning...

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