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Standard XII

Mathematics

Applications of Cross Product

Three masses ...

Question

Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side a. The $x$ coordinate of the centre of mass is :

\frac{7}{12} a

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\frac{5}{9} a

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\frac{7 \sqrt{2}}{9} a

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\frac{\sqrt{5}}{9} a

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Solution

The correct option is B $\frac{5}{9} a$
The x coordinates of masses $2 k g, 3 k g, 4 k g$ are $0, a, a / 2$ respectively.

So the x coordinates of COM is

$\frac{2 \times 0 + 3 \times a + 4 \times (a / 2)}{(2 + 3 + 4)} = 5 a / 9$

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Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side a. The x coordinate of the centre of mass is :

The correct option is B 59aThe x coordinates of masses 2kg,3kg,4kg are 0,a,a/2 respectively. So the x coordinates of COM is 2×0+3×a+4×(a/2)(2+3+4)=5a/9

Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side a. The $x$ coordinate of the centre of mass is :

The correct option is B $\frac{5}{9} a$
The x coordinates of masses $2 k g, 3 k g, 4 k g$ are $0, a, a / 2$ respectively.

So the x coordinates of COM is

$\frac{2 \times 0 + 3 \times a + 4 \times (a / 2)}{(2 + 3 + 4)} = 5 a / 9$