Question with Solution
With the discovery of phenomenon of gravitation and the formulation of Newton's law of gravitation, the major challenge for the physicists was to find and explain the reason behind the gravitational interaction. Fatio and Le Sage proposed an explanation for the gravitational interaction. According to them, the entire universe is filled with streams of tiny unseen particles called ultra mundane corpuscle moving uniformly in all directions. Consider a single object placed in free space. This object will be struck by the ultra mundane corpuscle from all directions moving with same speeds. The object experiences uniform push from all sides, so that net force is zero. But the presence of this object can be felt by other objects by the fact that the second object will be shadowed by the first object. The path of ultramundane particles moving towards the second object will be obstructed by the first object. So the second object will receive a lesser number of corpuscles from the direction of first object. The force exerted by the corpuscles on second object will not remain same in all directions. Infect, if will decrease from the direction of first object. So the force of attraction can be explained as a diminished push on the second object from the direction of first.
\caption{Isolated object (net force )}
\caption{Two objects attract each other}
Mass proportionality : From the given theory, it seems that the shadow effect or the gravitational pull will be proportional to surface area instead of mass. But gravity is proportional to the masses. To satisfy the need for mass proportionality, Fatio proposed that (A) the basic elements of matter are very small so that gross matter consists mostly of empty space, and (B) that the particles are so small, that only a small fraction of them would be intercepted by gross matter. The result is, that the "shadow" of each body is proportional to the surface of every single element of matter. If it is then assumed that the elementary opaque elements of all matter are identical (i.e., having the same ratio of density to area), it will follow that the shadow effect is, at least approximately, proportional to the mass. (Assume, Newtonian mechanics is applicable here)
Assume that ultra mundane corpuscles carry an average translational kinetic energy, K and their volume density (number per unit volume) is N. In the above theory if we assume collisions of ultra mundane corpuscles to be perfectly elastic, the pressure experienced by an isolated body due to collisions with ultra mundane corpuscles is
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All directions are symmetrical Question No. 25 and 26 Two uniform spherical stars made of same material have radii R and 2R. Mass of the smaller planet is m . They start moving from rest towards each other from a large distance under mutual force of gravity. The collision between the stars is inelastic with coefficient of restitution 1/2.
