Question

Two men, of masses $60$ kg and $80$ kg are sitting at the ends of a boat of mass $60$ kg and length $4$ m. The boat is stationary. If the men now exchange their positions, then?

• A. The centre of mass of the two men shifts by $2$ m
• B. The boat moves by $0.4$ m
• C. The centre of mass of the two men shifts by $4/7$ m
• D. The boat moves by $0.6$ m

Answer 1

The correct option is B The boat moves by $0.4$ m

Let X be the center of mass from 60 kg, assuming torque at X

$60X=60(2-X)+80(4-X)$

$60X=120X-60X+320-80X$

$200X=440$

$X=\frac{11}{5}$

Similarly when they interchange their position with each other

$80X=60(2-X)+60(4-X)$

$80X=120-60X+240-60X$

$200X=360$

$X_{inetr}=\frac{9}{5}$

Thus by interchanging their position the center of mass shifts

$X_{shift}=\frac{11}{5}-\frac{9}{5}$=$\frac{2}{5}$=0.4 m