Plz be thorough. Thanks An experiment is performed in deep space where two masse

Question

Plz be thorough. Thanks

An experiment is performed in deep space where two masses, one 50.0 kg and the other 250-kg are released. Both have a radius of 0.20 m. The spheres are released from rest at a distance from center to center of 20.0 m apart. They begin to accelerate due to mutual gravitational attraction. Ignore all other forces. Linear momentum is constant. Explain why. When the centers are 10.0 m apart, find the speeds of both spheres. How far from the initial position of the 50.0 kg sphere will the two spheres collide?

Explanation / Answer

(i) The force acting on the bodies independently are same in magnitude but opposite in direction

So net force on the system as a whole =0

As net external force is 0, so linear momentum will remain conserved

(ii)Initial Potential energy=Kinetic energy + Final Pot. Energy

So

-GMm/20=KE-GMm/10

So

KE=GMm/20

KE=0.5mv^2+0.5MV^2

and mv=MV (momentum conservation)

So

0.5mv^2(M+m)/M=GMm/20

So

v=3.73*10^-5m/s and V=7.455*10^-6 m/s

(iii)on collision r=0.4m

COM does not move as there is no ext force.

So we can calulate the initial position of the COM

let is be at a distance x from mass m

So

x=(M*20)/(m+M)=16.67 meters

Finally when they are at a distance r=0.4

then

x'(dist from center of m)=M*0.4/(M+m)=0.33 meters

So

Distance moved=16.67-0.33=16.33meters

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