Two balls A and B of masses 100 gm and 250 | vedclass

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Question

(A) Since the spring force is an internal force,the net external force on the system is zero.Therefore,the acceleration of the center of mass is zero:

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$25 \ cm/s^2$ towards the east

Vedclass · Answer

(A) Since the spring force is an internal force,the net external force on the system is zero.Therefore,the acceleration of the center of mass is zero: $M_A \vec{a}_A + M_B \vec{a}_B = 0$.Given: $M_A = 100 \ gm = 0.1 \ kg$,$M_B = 250 \ gm = 0.25 \ kg$.Acceleration of ball $B$,$\vec{a}_B = 10 \ cm/s^2$ (West).Using the equation: $\vec{a}_A = -\frac{M_B}{M_A} \vec{a}_B$.$\vec{a}_A = -\frac{0.25 \ kg}{0.10 \ kg} 	imes (10 \ cm/s^2 	ext{ West})$.$\vec{a}_A = -2.5 	imes (10 \ cm/s^2 	ext{ West}) = -25 \ cm/s^2 	ext{ West}$.Since the negative sign indicates the opposite direction,$\vec{a}_A = 25 \ cm/s^2$ towards the east.

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