Two bodies of mass 1 kg and 3 kg have position vectors ̂i+2̂j+̂k and -3̂i-2̂j+̂k respectively. The magnitude of the position vector of the centre of mass of this system is equal in magnitude to the vector

Question

Accepted Answer

(1) ̂i+2̂j+̂k. ⃗r_cm=(1(̂i+2̂j+̂k)+3(-3̂i-2̂j+̂k))/(1+3)=(-8̂i-4̂j+4̂k)/4=-2̂i-̂j+̂k. Its magnitude is √4+1+1=√6. Option (d) -2̂i-̂j+2̂k has magnitude √4+1+4=3; only option (a) ̂i+2̂j+̂k has magnitude √1+4+1=√6, matching ⃗r_cm.

Two bodies of mass 1 kg and 3 kg have position vectors ̂i+2̂j+̂k and -3̂i-2̂j+̂k respectively. The magnitude of the position vector of the centre of mass of this system is equal in magnitude to the vector

Step-by-step solution

Why the other options are wrong