Three point particles of masses $1.0\,\text{kg}$, $1.5\,\text{kg}$ and $2.5\,\text{kg}$ are placed at three corners of a right angle triangle of sides $4.0\,\text{cm}$, $3.0\,\text{cm}$ and $5.0\,\text{cm}$ as shown in the figure. The centre of mass of the system is at a point:

(D) 0.9 cm right and 2.0 cm above 1 kg mass.

(A) 0.6 cm right and 2.0 cm above 1 kg mass.

(B) 2.0 cm right and 0.9 cm above 1 kg mass.

(C) 1.5 cm right and 1.2 cm above 1 kg mass.

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Conservation of Momentum

Three point particles of masses

1.0 kg

1.5 kg

and

2.5 kg

are placed at three corners of a right angle triangle of sides

4.0 cm

3.0 cm

and

5.0 cm

as shown in the figure. The centre of mass of the system is at a point:

Answer: (D)

Place the

1 kg

mass at the origin, the

1.5 kg

mass at

(3, 0)

and the

2.5 kg

mass at

(0, 4)

, matching the

3

–

4

–

5

right triangle. Then

X_{cm} = \frac{1 ( 0 ) + 1.5 ( 3 ) + 2.5 ( 0 )}{5} = \frac{4.5}{5} = 0.9 cm

and

Y_{cm} = \frac{1 ( 0 ) + 1.5 ( 0 ) + 2.5 ( 4 )}{5} = \frac{10}{5} = 2.0 cm

, so the centre of mass lies

0.9 cm

to the right of and

2.0 cm

above the

1 kg

mass.

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option