JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Conservation of Momentum

Two bodies of mass 1 kg and 3 kg have position vector

\hat{i} + 2 \hat{j} + \hat{k}

and

- 3 \hat{i} - 2 \hat{j} + \hat{k}

respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

Answer: (A)

Solution

The position vector of the center of mass is

r_{com} = \frac{m _{1} r _{1} + m _{2} r _{2}}{m _{1} + m _{2}} = \frac{1 ( i ^ + 2 j ^ + k ^ ) + 3 ( - 3 i ^ - 2 j ^ + k ^ )}{1 + 3} = \frac{i ^ + 2 j ^ + k ^ - 9 i ^ - 6 j ^ + 3 k ^}{4} = \frac{- 8 i ^ - 4 j ^ + 4 k ^}{4} = - 2 \hat{i} - \hat{j} + \hat{k}

. The magnitude is

∣ r_{com} ∣ = 4 + 1 + 1 = 6

. Checking option (A):

∣ \hat{i} - 2 \hat{j} + \hat{k} ∣ = 1 + 4 + 1 = 6

. The magnitudes match.

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Single correct option