A boat of mass 100 kg and length 6 m carries two persons of masses 60 kg and 40 kg, initially standing at opposite ends. They exchange their positions. Neglect horizontal external forces. If the magnitude of displacement of the boat is N/5 m, find N.
Physics · Center of maas , Momentum and Collision · center of mass and question based on it
JEE Mains NEET JEE Advanced

Question

A boat of mass 100 kg and length 6 m carries two persons of masses 60 kg and 40 kg, initially standing at opposite ends. They exchange their positions. Neglect horizontal external forces. If the magnitude of displacement of the boat is N/5 m, find N.

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

G1 Physics · Accepted Answer

Take the boat centre as the origin in the boat frame. Initially let the 60 kg person be at x = −3 m and the 40 kg person at x = +3 m. Their initial moment relative to the boat is 60(−3)+40(3)=−60 kg·m. After exchange, the moment is 60(3)+40(−3)=+60 kg·m. Thus the internal first moment changes by +120 kg·m. If the entire boat-plus-persons system of total mass 200 kg shifts by X relative to water, conservation of the system COM gives 200X + 120 = 0. Therefore X = −0.6 m. Its magnitude is 0.6 = 3/…