Rotational Motion Question 49
Question: A rod is of length 3 m and its mass acting per unit length is directly proportional to distance x from its one end. The centre of gravity of the rod from that end will be at:
[AIPMT 2002]
Options:
A) 1.5 m
B) 2.0 m
C) 2.5 m
D) 3.0 m
Show Answer
Answer:
Correct Answer: A
Solution:
- Position of centre of gravity of a continuous body is given by
A rod lying along any of coordinate axes serves for us as continuous body.
Suppose a rod of mass M and length L is lying along die x-axis with its one end x=0
Mass per unit length of the rod
Hence, the mass of the element PQ of length
The co-ordinates of the element PQ are
but as given,
The y-co-ordinate of centre of gravity
Similarly,
i.e., the co-ordinates of centre of gravity of n rod are (1.5, 0, 0) or it lies at distance 1.5 m from one end.
