Two masses, 1 kg and 3 kg, have position vectors ( $\hat{i}+2\hat{j}+\hat{k}$ ) m and ( $-3\hat{i}-2\hat{j}+\hat{k}$ ) m respectively. Find the position vector of their centre of mass.
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Question

Two masses, 1 kg and 3 kg, have position vectors ( i ^ + 2 j ^ + k ^ \hat{i}+2\hat{j}+\hat{k} i ^ + 2 j ^ + k ^ ) m and ( − 3 i ^ − 2 j ^ + k ^ -3\hat{i}-2\hat{j}+\hat{k} − 3 i ^ − 2 j ^ + k ^ ) m respectively. Find the position vector of their centre of mass.

Physics · Center of maas , Momentum and Collision · center of mass and question based on it

AIPMT Screening 2009 NEET

G1 Physics · Accepted Answer

Step 1: Use centre-of-mass position vector=(m₁r₁+m₂r₂)/(m₁+m₂). Step 2: Numerator=(i+2j+k)+3(-3i-2j+k)=-8i-4j+4k. Step 3: Divide by 4 to get -2i-j+k. Final answer: B — -2i-j+k.

Two masses, 1 kg and 3 kg, have position vectors ( i ^ + 2 j ^ + k ^ \hat{i}+2\hat{j}+\hat{k} i ^ + 2 j ^ ​ + k ^ ) m and ( − 3 i ^ − 2 j ^ + k ^ -3\hat{i}-2\hat{j}+\hat{k} − 3 i ^ − 2 j ^ ​ + k ^ ) m respectively. Find the position vector of their centre of mass.

Two masses, 1 kg and 3 kg, have position vectors ( i ^ + 2 j ^ + k ^ \hat{i}+2\hat{j}+\hat{k} i ^ + 2 j ^ + k ^ ) m and ( − 3 i ^ − 2 j ^ + k ^ -3\hat{i}-2\hat{j}+\hat{k} − 3 i ^ − 2 j ^ + k ^ ) m respectively. Find the position vector of their centre of mass.