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7.Gravitation
hard
A mass $m$ , travelling at speed $V_0$ in a straight line from far away is deflected when it passes near a black hole of mass $M$ which is at a perpendicular distance $R$ from the original line of flight. $a$ , the distance of closest approach between the mass and the black hole is given by the relation
A
$a = R{\left( {1 + \frac{{2GM}}{{aV_0^2}}} \right)^{1/2}}$
B
$a = R{\left( {1 + \frac{{aV_0^2}}{{2GM}}} \right)^{1/2}}$
C
$a = R{\left( {1 + \frac{{GM}}{{2aV_0^2}}} \right)^{ - 1/2}}$
D
$a = R{\left( {1 + \frac{{2GM}}{{aV_0^2}}} \right)^{ - 1/2}}$
Solution
$\mathrm{mv}_{0} \mathrm{R}=\mathrm{mva}$ $…(i)$
$\frac{1}{2} \mathrm{mv}_{0}^{2}=\frac{1}{2} \mathrm{mv}^{2}-\frac{\mathrm{GMm}}{\mathrm{a}}$ $…(2)$
Standard 11
Physics
