A square plank of mass m₁ = 100 kg and edge length L = 2√2 m is placed on a smooth surface. Two persons each of mass m₂ = m₃ = 50 kg are at corners of a plank as shown in figure. Two persons begin walk on the plank along two different paths as shown in figure and reach nearest corners. If the magnitude of displacement of plank (in m) in the process is 5 × z, find z.
Physics · Mixed Chapter
JEE Mains

Question

A square plank of mass m₁ = 100 kg and edge length L = 2√2 m is placed on a smooth surface. Two persons each of mass m₂ = m₃ = 50 kg are at corners of a plank as shown in figure. Two persons begin walk on the plank along two different paths as shown in figure and reach nearest corners. If the magnitude of displacement of plank (in m) in the process is 5 × z, find z.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The smooth ground exerts no horizontal force; the combined centre of mass remains fixed. The total mass is 100+50+50=200 kg. Step 2: From the figure, one person walks one side length L in x and the other walks one side length L in y relative to the plank. Step 3: Plank displacement vector is −(50/200)L î−(50/200)L ĵ, whose magnitude is (L/4)√2=1 m since L=2√2 m. Step 4: As stated, 5z=1 and z=0.2. The printed answer 1 appears to give the plank displacement rather than z and is not consis…