Rotational Motion Question 142
Question: The mass per unit length of a non-uniform rod of length L varies as $m=\lambda x$ where $\lambda $ is constant. The centre of mass of the rod will be at:
Options:
A) $\frac{2}{3}L$
B) $\frac{3}{2}L$
C) $\frac{1}{2}L$
D) $\frac{4}{3}L$
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $X _{cm}=\int _{0}^{L}{\frac{(dm)x}{\int _{0}^{L}{(dm)}}=\frac{\int _{0}^{L}{(\lambda xdx)x}}{\int _{0}^{L}{(\lambda xdx)}}}=\frac{2L}{3}~~$
