A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :
(1) $\frac { \mathrm { GmM } \pi ^ { 2 } } { \mathrm {~L} ^ { 2 } }$
(2) $\frac { \mathrm { GMm } \pi } { 2 \mathrm {~L} ^ { 2 } }$
(3) 0
(4) $\frac { 2 \mathrm { GmM } \pi } { \mathrm { L } ^ { 2 } }$