A system consists of three particles, each of mass m and located at (1,1),(2,2) and (3,3). The co-ordinates of the centre of mass are

Correct answer: B. (2,2) The coordinates of C.M of three particle are array c x= m_ 1 x_ 1 +m_ 2 x_ 2 +m_ 3 x_ 3 m_ 1 +m_ 2 +m_ 3 & y= m_ 1 y_ 1 +m_ 2 y_ 2 +m_ 3 y_ 3 m_ 1 +m_ 2 +m_ 3 here m_ 1 =m_ 2 =m_ 3 =m so x= (x_ 1 +x_ 2 +x_ 3 ) m m+m+m =2 array y= (y_ 1 +y_ 2 +y_ 3 ) m m+m+m =2 so coordinates of C . M . of three particle are (2,2) V=300 m / s

BITSAT 2010

Exam: BITSAT
Year: 2010
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

BITSAT 2010 · Physics · Center of Mass, Momentum and Collision

A system consists of three particles, each of mass m and located at...

A system consists of three particles, each of mass

\mathrm{m}

and located at (1,1),(2,2) and (3,3). The co-ordinates of the centre of mass are

Options

A(1,1)
B(2,2)
C(3,3)
D(6,6)

Correct answer

B. (2,2)

Step-by-step solution

The coordinates of C.M of three particle are

\begin{array}{c}\mathrm{x}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{ m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}& \mathrm{y}=\frac{\mathrm{m}_{1} \mathrm{y}_{1}+\mathrm{m}_{2} \mathrm{y}_{2}+\mathrm{m}_{3} \mathrm{y}_{3}}{\mathrm{ m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}\\ \text{ here } \mathrm{m}_{1}=\mathrm{m}_{2}=\mathrm{m}_{3}=\mathrm{m}\\ \text{ so } \mathrm{x}=\frac{\left(\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}\right) \mathrm{m}}{\mathrm{m}+\mathrm{m}+\mathrm{m}}=2 \end{array}

y=\frac{\left(y_{1}+y_{2}+y_{3}\right) m}{m+m+m}=2 so coordinates of \mathrm{C} . \mathrm{M}

. of three particle are (2,2)

\mathrm{V}=300 \mathrm{ m} / \mathrm{s}$

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