Three small spheres A , B and C of masses 50g.100g and 150g are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The (.x,y.) coordinates of the centre of mass will be:

Question

Three small spheres A , B and C of masses 50g.100g and 150g are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The (.x,y.) coordinates of the centre of mass will be: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-mmw38u7z1ntbmie9.jpg" /> (A) ((7/12) m (√3/4) m) (B) ((7/12) m , (√3/8) m) (C) ((√3/4) m , (5/12) m) (D) ((√3/8) m (7/12) m)

Tardigrade Admin · Accepted Answer

xcm=(50 × 0 + 100 × 1 + 150 × 1 / 2/50 + 100 + 150) =(175/300)=(7/12)cm ycm=(50 × 0 + 100 × 0 + 150 √3 / 2/300)=(√3/4)cm

Q. Three small spheres A , B and C of masses $50 g .100 g$ and $150 g$ are placed at the vertices of an equilateral triangle of side $1 m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be:

$(\frac{7}{12} m \frac{3}{4} m)$

$(\frac{7}{12} m, \frac{3}{8} m)$

$(\frac{3}{4} m, \frac{5}{12} m)$

$(\frac{3}{8} m \frac{7}{12} m)$

$x_{c m} = \frac{50 \times 0 + 100 \times 1 + 150 \times 1/2}{50 + 100 + 150}$
$= \frac{175}{300} = \frac{7}{12} c m$
$y_{c m} = \frac{50 \times 0 + 100 \times 0 + 150 3 /2}{300} = \frac{3}{4} c m$

Q. Three small spheres A , B and C of masses 50g.100g and 150g are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The (x,y) coordinates of the centre of mass will be:

(127​m43​​m)

(127​m,83​​m)

(43​​m,125​m)

(83​​m127​m)