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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. The centre of mass of the system is at a point

Asked in JEE Main 7th Jan 1st Shift 2020 · Discrete systems and motion of the centre of mass

Figure: Discrete systems and motion of the centre of mass
Answer: (2) 0.9 cm right and 2.0 cm above the 1 kg mass

Step-by-step solution

Put the 1 kg at the right-angle corner as origin, the 1.5 kg along x at 3 cm (base) and the 2.5 kg along y at 4 cm.

x_cm=(1.5×3)/(1+1.5+2.5)=(4.5)/5=0.9 cm.

y_cm=(2.5×4)/5=(10)/5=2.0 cm.

So the centre of mass is 0.9 cm right and 2.0 cm above the 1 kg mass.

Why the other options are wrong

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