JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Conservation of Momentum

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Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be

x m

. The value of x is

Answer: 2

Solution

Place the origin at the right angle. The three masses are at positions

(0, 0)

(3, 0)

, and

(0, 3)

.

Center of mass position:

r_{com} = \frac{M ( 0 i ^ + 0 j ^ ) + M ( 3 i ^ + 0 j ^ ) + M ( 0 i ^ + 3 j ^ )}{3 M} = \frac{3 i ^ + 3 j ^}{3} = \hat{i} + \hat{j}

Magnitude:

∣ r_{com} ∣ = 1^{2} + 1^{2} = 2

Therefore,

x = 2

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Integer answer

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