Question

A point $\rho$ lies on the axis of a ring of mass M and radius $\alpha$, at a distance $\alpha$, from its centre C, A small particle starts from $\rho$ and reaches C under gravitational attraction only.Its speed at C will be

• A. $\sqrt{\frac{2GM}{\alpha }}$
• B. $\sqrt{\frac{2GM}{\alpha }}(1-\frac{1}{\sqrt{2}})$
• C. $\sqrt{\frac{2GM}{\alpha }}(\sqrt{2}-1)$
• D. Zero

Answer 1

The correct option is B

$\sqrt{\frac{2GM}{\alpha }}(1-\frac{1}{\sqrt{2}})$

Increase in KE = decrease in PE

$\therefore$ $\frac{1}{2}m{v}^2=m(V_i-V_f)$

$\therefore$ $v=\sqrt{2(V_i-V_f)}$

=$\sqrt{2[-\frac{GM}{\sqrt{2}\alpha }+\frac{GM}{\alpha }]}$

= $\sqrt{\frac{2GM}{\alpha }(1-\frac{1}{\sqrt{2}})}$