Rotational Motion Question 106
Question: The centre of mass of a non-uniform rod of length $ L $ whose mass per unit length $ \lambda $ varies as $ \lambda =\frac{k.x^{2}}{L} $ where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)
Options:
A) $ \frac{3}{4}L $
B) $ \frac{1}{4}L $
C) $ \frac{k}{L} $
D) $ \frac{3k}{L} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a]
$ \therefore x _{c m} \frac{\int_0^L \frac{K}{L} x^2 d x \cdot x}{\int_0^L \frac{K}{L} x^2 d x}=\frac{\left.\frac{x^4}{4}\right|_0 ^L}{\left.\frac{x^3}{3}\right|_0 ^L}=\frac{3}{4} L $
