Two identical bodies A and B have equal masses. Their initial velocities are $V_{A}$ = 4î m·s⁻¹ and $V_{B}$ = 4ĵ m·s⁻¹, respectively. Body A has constant acceleration $a_{A}$ = 6î + 6ĵ m·s⁻², while body B has zero acceleration. What is the path followed by the centre of mass of the two-body system?
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Question

Two identical bodies A and B have equal masses. Their initial velocities are $V_{A}$ = 4î m·s⁻¹ and $V_{B}$ = 4ĵ m·s⁻¹, respectively. Body A has constant acceleration $a_{A}$ = 6î + 6ĵ m·s⁻², while body B has zero acceleration. What is the path followed by the centre of mass of the two-body system?

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G1 Physics · Accepted Answer

For equal masses, v(CM) = [v(A)+v(B)] ÷ 2. Thus, v(CM) = [4î+4ĵ] ÷ 2 = 2î+2ĵ. Similarly, a(CM) = [a(A)+a(B)] ÷ 2 = [6î+6ĵ] ÷ 2 = 3î+3ĵ. The centre-of-mass velocity and acceleration are parallel because v(CM) is parallel to a(CM). Hence the direction of motion does not change, and the centre of mass moves along a straight line. Correct option: C.