Four particles of masses m, m, 2m and 2m are placed at the four corners of a square of side a as shown in the figure. The (x, y) coordinates of the centre of mass are

$(\frac{a}{2}, 2 a)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(\frac{a}{2}, a)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(\frac{a}{2}, \frac{2 a}{3})$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$(a, \frac{a}{3})$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$(\frac{a}{2}, \frac{2 a}{3})$

The (x, y) co-ordinates of the centre of mass are given by
$x = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3} + m_{4} x_{4}}{m_{1} + m_{2} + m_{3} + m_{4}} = \frac{m \times 0 + m \times a + 2 m \times a + 2 m \times 0}{m + m + 2 m + 2 m} = \frac{a}{2}$
and $y = \frac{m_{1} y_{1} + m_{2} y_{2} + m_{3} y_{3} + m_{4} y_{4}}{m_{1} + m_{2} + m_{3} + m_{4}} = \frac{m \times 0 + m \times 0 + 2 m \times a + 2 m \times a}{m + m + 2 m + 2 m} = \frac{2 a}{3}$
Hence, the correct choice is (c).

Suggest Corrections

Similar questions

Four particles of masses m, m, 2m and 2m are placed at the four corners of a square of side a as shown in the figure. The (x, y) coordinates of the centre of mass are

Q. Four particles of masses 'm', 'm', '2m' and '2m' are placed at the four corners of a square of side a as shown in diagram The (x, y) coordinates of the centre of mass are

Q. Four particles of masses

m, m, 2 m

and

2 m

are placed at the four corners of a square of side

a

as shown in the figure. The magnitude of the gravitational force acting on a particle of mass

m

placed at the centre of the square is

Q. Four particles of masses m,2m, 3m ,4m are placed at the corners of a square of side 'a' as shown in the figure. Find out the co-ordinates of centre of mass.

Join BYJU'S Learning Program

Four particles of masses m, m, 2m and 2m are placed at the four corners of a square of side a as shown in the figure. The (x, y) coordinates of the centre of mass are

The correct option is C (a2,2a3) The (x, y) co-ordinates of the centre of mass are given by x=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4=m×0+m×a+2m×a+2m×0m+m+2m+2m=a2 and y=m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4=m×0+m×0+2m×a+2m×am+m+2m+2m=2a3 Hence, the correct choice is (c).