A particle is projected from the surface of one star towards other star of same radius a and mass with such a minimum velocity KGMa. so that it is attracted towards other star. Find the value of K if two stars are 2r distance apart:

12mvmin2 = [-GMmr-GMmr]-[-GMm(2r-a)-GMma] = 2GMm(a2-2ar+r2)ar(2r-a)or vmin = GMa×2(r-a)[r(2r-a)]12So, K = 2(r-a)[r)(2r-a)]12

A particle is projected from the surface of one star towards other star of same radius a and mass with such a minimum velocity KGMa. so that it is attracted towards other star. Find the value of K if two stars are 2r distance apart:

12mvmin2 = [-GMmr-GMmr]-[-GMm(2r-a)-GMma] = 2GMm(a2-2ar+r2)ar(2r-a)or vmin = GMa×2(r-a)[r(2r-a)]12So, K = 2(r-a)[r)(2r-a)]12

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A particle is projected from the surface of one star towards other star of same radius a and mass with such a minimum velocity $K \sqrt{\frac{GM}{a}}$ . so that it is attracted towards other star. Find the value of K if two stars are 2r distance apart:

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$\frac{2 (r - a)}{{[r (2 r - a)]}^{\frac{1}{2}}}$

$\frac{2 (r - a)}{{[r (r - a)]}^{\frac{1}{2}}}$

$\frac{r - a}{{[r - (r - a)]}^{\frac{1}{2}}}$

$\frac{r + a}{{[r - (r - a)]}^{\frac{1}{2}}}$

answer is A.

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$\frac{1}{2} {mv}_{\min}^{2} = [- \frac{GMm}{r} - \frac{GMm}{r}] - [- \frac{GMm}{(2 r - a)} - \frac{GMm}{a}]$

= $\frac{2 GMm (a^{2} - 2 ar + r^{2})}{ar (2 r - a)}$

or $v_{\min} = \sqrt{\frac{GM}{a}} \times \frac{2 (r - a)}{{[r (2 r - a)]}^{\frac{1}{2}}}$

So, $K = \frac{2 (r - a)}{{[r) (2 r - a)]}^{\frac{1}{2}}}$

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A particle is projected from the surface of one star towards other star of same radius a and mass with such a minimum velocity KGMa. so that it is attracted towards other star. Find the value of K if two stars are 2r distance apart:

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A particle is projected from the surface of one star towards other star of same radius a and mass with such a minimum velocity $K \sqrt{\frac{GM}{a}}$ . so that it is attracted towards other star. Find the value of K if two stars are 2r distance apart: