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QAIPM-2002-Ph-2806: NEET 2002 Physics - Class 11 AIPM-2002-Ph-2806 Solution: A rod of length is 3 m and its mass acting per unit length is…
A rod of length is 3 m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at:
Multiple Choice Options
- A 1.5 m
- B 2 m
- C 2.5 m
- D 3.0 m.
Step-by-Step Verified Solution
Let us consider an elementary length dx at a distance x from one end.
It�s mass = k �x �dx
[k = proportionality constant]
Then centre of gravity of the rod x c is given by
x c = � 0 3 k x d x . x � 0 3 k x d x = � 0 3 x 2 d x � 0 3 x d x = x 3 3 | 0 3 x 2 2 | 0 3
_ x c = 27 3 9 2 = 2
_ Centre of gravity of the rod will be at distance of 2 m from one end.