System of Particles and Rotational Motion - Result Question 4
4. Three masses are placed on the $x$-axis : $300 g$ at origin, $500 g$ at $x=40 cm$ and $400 g$ at $x=$ $70 cm$. The distance of the centre of mass from the origin is :
[2012M]
(a) $40 cm$
(b) $45 cm$
(c) $50 cm$
(d) $30 cm$
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Answer:
Correct Answer: 4. (a)
Solution:
$ \text{ (a) } \begin{aligned} X _{cm} & =\frac{m_1 x_1+m_2 x_2+m_3 x_3}{m_1+m_2+m_3} \\ X _{cm} & =\frac{300 \times(0)+500(40)+400 \times 70}{300+500+400} \\ X _{cm} & =\frac{500 \times 40+400 \times 70}{1200} \\ X _{cm} & =\frac{50+70}{3}=\frac{120}{3}=40 cm \end{aligned} $
