Question

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

• A. $v = \frac { 1 } { 2 R } \sqrt { \frac { 1 } { G m } }$
• B. $v = \sqrt { \frac { G m } { 2 R } }$
• C. $v = \frac { 1 } { 2 } \sqrt { \frac { G m } { R } }$
• D. $v = \sqrt { \frac { 4 G m } { R } }$

Answer 1

Answer: (C)

$v = \frac { 1 } { 2 } \sqrt { \frac { G m } { R } }$

Answer 2

Both the particles moves diametrically opposite position along the circular path of radius $R$ and the gravitational force provides required centripetal force

$\frac { m v ^ { 2 } } { R } = \frac { G m m } { ( 2 R ) ^ { 2 } }$ $\Rightarrow$ $v = \frac { 1 } { 2 } \sqrt { \frac { G m } { R } }$