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Numerical from centre of mass

Two skaters, one with Mass 45kg, 2’nd with Mass of 65kg stand on an ice rink holding a pole with L=10m with negligible mass. starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 45kg skater move?
Hint: They will meet at the centre of mass of the system.

If the 45 kg skater moves by x m, then the second one travels (10-x)m

then,

45 x = 65(10-x)

Solve and get the value for x

Centre of mass of an accelerated body

“What is the effect on centre of mass of system of particles when it is placed in accelerated train?” Vimal asked

A numerical from Centre of mass

Two objects, of mass 1 kg and 2 kg, are moving with velocities equal to +2 m/sec and -3 m/sec. The center of mass of the two objects is moving at velocity

=(1×2+2x(-3)/(1+2)=(2-6)/3=-4/3=-1.33 m/s (-ve sign shows that the centre of mass will be moving in the direction of the second body)

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