A 3 kg mass at r ⃗ 1 \vec{r}_1 r 1 = (2 i ^ + 5 j ^ \hat{i}+5\hat{j} i ^ + 5 j ^ )m is connected by a massless rod to a 2 kg mass at r ⃗ 2 \vec{r}_2 r 2 = (4 i ^ + 2 j ^ \hat{i}+2\hat{j} i ^ + 2 j ^ )m. The rod length and centre-of-mass coordinates are:
Physics · Center of maas , Momentum and Collision · center of mass and question based on it
JEE Advanced

Question

A 3 kg mass at r ⃗ 1 \vec{r}_1 r 1 ​ = (2 i ^ + 5 j ^ \hat{i}+5\hat{j} i ^ + 5 j ^ ​ )m is connected by a massless rod to a 2 kg mass at r ⃗ 2 \vec{r}_2 r 2 ​ = (4 i ^ + 2 j ^ \hat{i}+2\hat{j} i ^ + 2 j ^ ​ )m. The rod length and centre-of-mass coordinates are:

G1 Physics · Accepted Answer

Use x(COM) = Σmᵢxᵢ/Σmᵢ and y(COM) = Σmᵢyᵢ/Σmᵢ. Apply symmetry or the negative-mass method where material is removed. Substitution gives A: √13 m and (14/5, 19/5).

A 3 kg mass at r ⃗ 1 \vec{r}_1 r 1 ​ = (2 i ^ + 5 j ^ \hat{i}+5\hat{j} i ^ + 5 j ^ ​ )m is connected by a massless rod to a 2 kg mass at r ⃗ 2 \vec{r}_2 r 2 ​ = (4 i ^ + 2 j ^ \hat{i}+2\hat{j} i ^ + 2 j ^ ​ )m. The rod length and centre-of-mass coordinates are:

A 3 kg mass at r ⃗ 1 \vec{r}_1 r 1 = (2 i ^ + 5 j ^ \hat{i}+5\hat{j} i ^ + 5 j ^ )m is connected by a massless rod to a 2 kg mass at r ⃗ 2 \vec{r}_2 r 2 = (4 i ^ + 2 j ^ \hat{i}+2\hat{j} i ^ + 2 j ^ )m. The rod length and centre-of-mass coordinates are: