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

Correct answer: A. 40 ~cm aligned x_ CM & =(m_1 x_1+m_2 x_2+m_3 x_3)/(m_1+m_2+m_3) & =(300(0)+500(40)+400(70))/(300+500+400) & =(20000+28000)/(1200) & =(48000)/(1200) & =40 ~cm aligned

NEET 2012

Exam: NEET
Year: 2012
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

NEET 2012 · Physics · Center of Mass, Momentum and Collision

Three masses are placed on the x -axis : 300 ~g at origin, 500 ~g...

Three masses are placed on the

x

-axis :

300 \mathrm{~g}

at origin,

500 \mathrm{~g}

x=40 \mathrm{~cm}

and

400 \mathrm{~g}

x=70 \mathrm{~cm}

. The distance of the centre of mass from the origin is

Options

A $40 \mathrm{~cm}$
B $45 \mathrm{~cm}$
C $50 \mathrm{~cm}$
D $30 \mathrm{~cm}$

Correct answer

A. $40 \mathrm{~cm}$

Step-by-step solution

\begin{aligned}x_{\mathrm{CM}} & =\frac{m_1 x_1+m_2 x_2+m_3 x_3}{m_1+m_2+m_3}\\ & =\frac{300(0)+500(40)+400(70)}{300+500+400}\\ & =\frac{20000+28000}{1200}\\ & =\frac{48000}{1200}\\ & =40 \mathrm{~cm} \end{aligned}

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