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JEE Advanced 2009Paper 1
Exam
JEE Advanced
Year
2009
Paper
Paper 1
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JEE Advanced 2009 · Paper 1 · Physics · Center of Mass, Momentum and Collision

Look at the drawing given in the figure, which has been drawn with...

Look at the drawing given in the figure, which has been drawn with ink of uniform line-thickness. Look at the drawing given in the figure, which has been drawn with ink of uniform line-thickness. The mass of ink used
The mass of ink used to draw each of the two inner circles, and each of the two line segments is mm. The mass of the ink used to draw the outer circle is 6 m6 \mathrm{~m}. The coordinates of the centres of the different parts are, outer circle 10 , 0)0), left inner circle (0,0)(0,0), right inner circle (a,a)(a, a), vertical line (0,0)(0,0) and horizontal line (0,−a)(0,-a). The yy-coordinate of the centre of mass of the ink in this drawing is

Options

  1. Aa10\frac{a}{10}
  2. Ba8\frac{a}{8}
  3. Ca12\frac{a}{12}
  4. Da3\frac{a}{3}

Correct answer

A. a10\frac{a}{10}

Step-by-step solution

yCM=m1y1+m2y2+m3y3+m4y4+m5y5m1+m2+m3+m4+m5=(6m)(0)+(m)(a)+m(a)+m(0)6m+m+m+m+m=a10y_{C M} \begin{gathered} =\frac{m_1 y_1+m_2 y_2+m_3 y_3+m_4 y_4+m_5 y_5}{m_1+m_2+m_3+m_4+m_5}\\ =\frac{(6 m)(0)+(m)(a)+m(a)+m(0)}{6 m+m+m+m+m}=\frac{a}{10} \end{gathered}
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