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Two masses m1 & m2 are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of d is :
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two masses m1 & m2 are initially at rest and are separated by a ve...
We use the energy balance
Initial potential energy equals final kinetic energy
Gm1m2/d=1mv12/2+1mv22/2
also, from the conservation of momentum we have
m1v1=m2v2
or
v1= m1v1/ m2
Substituting this we get
v1=√2Gm22/d(m1+m2)
Similarly, we have
v2= √2Gm12/ d(m1+m2)
Now as velocities are in opposite direction their relative velocity is v1−(−v2)=v1+v2
or
[2G(m1+m2)/ d]1/2
Initial potential energy equals final kinetic energy
Gm1m2/d=1mv12/2+1mv22/2
also, from the conservation of momentum we have
m1v1=m2v2
or
v1= m1v1/ m2
Substituting this we get
v1=√2Gm22/d(m1+m2)
Similarly, we have
v2= √2Gm12/ d(m1+m2)
Now as velocities are in opposite direction their relative velocity is v1−(−v2)=v1+v2
or
[2G(m1+m2)/ d]1/2
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Two masses m1 & m2 are initially at rest and are separated by a ve...
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Two masses m1 & m2 are initially at rest and are separated by a ve...
We use the energy balance
Initial potential energy equals final kinetic energy
Gm1m2/d=1mv12/2+1mv22/2
also, from the conservation of momentum we have
m1v1=m2v2
or
v1= m1v1/ m2
Substituting this we get
v1=√2Gm22/d(m1+m2)
Similarly, we have
v2= √2Gm12/ d(m1+m2)
Now as velocities are in opposite direction their relative velocity is v1−(−v2)=v1+v2
or
[2G(m1+m2)/ d]1/2
Initial potential energy equals final kinetic energy
Gm1m2/d=1mv12/2+1mv22/2
also, from the conservation of momentum we have
m1v1=m2v2
or
v1= m1v1/ m2
Substituting this we get
v1=√2Gm22/d(m1+m2)
Similarly, we have
v2= √2Gm12/ d(m1+m2)
Now as velocities are in opposite direction their relative velocity is v1−(−v2)=v1+v2
or
[2G(m1+m2)/ d]1/2
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Two masses m1 & m2 are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of d is :a)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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