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Two spherical bodies of mass M and 5M and radii R & 2R respectively are released in free space with initial separation between their centers equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
  • a)
    2.5 R
  • b)
    4.5 R
  • c)
    7.5 R
  • d)
    1.5 R
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two spherical bodies of mass M and 5M and radii R & 2R respectively a...
Are brought in contact with each other. What is the ratio of final to initial gravitational potential energy of the system?

We can start by using the formula for gravitational potential energy:

U = -Gm1m2/r

where U is the potential energy, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between them.

Initially, the two bodies are separated by a distance of 6R (the sum of their radii). The potential energy of the system is:

U1 = -G(M)(5M)/(6R) = -5GM^2/(6R)

When the two bodies are brought in contact with each other, they will merge to form a single spherical body with mass 6M and radius 2R. The final potential energy of the system is:

U2 = -G(6M)^2/(2R) = -18GM^2/R

The ratio of final to initial potential energy is:

U2/U1 = (-18GM^2/R)/(-5GM^2/(6R)) = 108/5

Therefore, the ratio of final to initial gravitational potential energy of the system is 108/5.
Free Test
Community Answer
Two spherical bodies of mass M and 5M and radii R & 2R respectively a...
Distance between their surfaces = 12R − R − 2R = 9R
Since,
P ∝ mass
a ∝ mass
Distance ∝ acceleration
So, we can write;
a1/a2 ​= m/5m ​= s1/s2
s1/s2​ ​ = 1/5
5s1 ​= 5s2 ​ .......................(1)
s1 ​+ s2 ​ = 9R .......................(2)
On solving these equations;
s1 ​= 1.5R
s2 ​= 7.5R
Since smaller balls have more acceleration in the same time interval, smaller balls will cover more distance.
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Two spherical bodies of mass M and 5M and radii R & 2R respectively are released in free space with initial separation between their centers equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision isa)2.5 Rb)4.5 Rc)7.5 Rd)1.5 RCorrect answer is option 'B'. Can you explain this answer?
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