Question

Locate the COM of following system of particle

• A. 45.5a
• B. 49.5a
• C. 50a
• D. None of these

Answer 1

The correct option is B 49.5a

There are $100$ particles so the center of mass will be $x=\frac{M(0+a+2a+3a+......99a)}{100M}=\frac{\frac{100}{2}(2\times 0+(100-1\left)a\right)}{100}=49.5a$

The formula used is the sum of $n$ terms of an $AP$ with first term $a$ and common difference as $d$ is given by

$Sum=\frac{n}{2}(2a+(n-1\left)d\right)$