2 bodies of different masses of 2 kg and 4 kg are moving with accelertions 20 m/s2 and 10 m/s2 towards each other due to mutual gravitational attraction. What is the acceleration of their centre of mass.

m1 =2kg, m2 =4kg, a→1=20 m/s2, a→2=−10 m/s2a→cm = m1a→1 + m2a→2 m2 + m2 = 2 × 20 −4 × 102+4 = 0 m/s2.

2 bodies of different masses of 2 kg and 4 kg are moving with accelertions 20 m/s2 and 10 m/s2 towards each other due to mutual gravitational attraction. What is the acceleration of their centre of mass.

m1 =2kg, m2 =4kg, a→1=20 m/s2, a→2=−10 m/s2a→cm = m1a→1 + m2a→2 m2 + m2 = 2 × 20 −4 × 102+4 = 0 m/s2.

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2 bodies of different masses of 2 kg and 4 kg are moving with accelertions 20 m/s² and 10 m/s² towards each other due to mutual gravitational attraction. What is the acceleration of their centre of mass.

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6 m/s²

8 m/s²

Zero

5 m/s²

answer is D.

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Detailed Solution

$\begin{array}{l} m_{1} = 2 kg, m_{2} = 4 kg, {\vec{a}}_{1} = 20 m / s^{2}, {\vec{a}}_{2} = - 10 m / s^{2} \\ {\vec{a}}_{cm} = \frac{m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2}}{m_{2} + m_{2}} = \frac{2 \times 20 - 4 \times 10}{2 + 4} = 0 m / s^{2} . \end{array}$