A sphere resting in a smooth V sthaped groove and subjected to a spring force, is shown in the figure. The spring is compressed to a length of 100mm from its freelength of 150mm. If the stiffness of spring K=2N/mm. the contant reaction `R_(L)` and `R_(M)` at the points L andM respectively are

Options

A. `R_(L)=121.24N` and `R_(M)=80N`
B. `R_(L)=121.24N` and `R_(M)=70N`
C. `R_(L)=131.24N` and `R_(M)=60N`
D. `R_(L)=131.24 N` and `R_(M)=80N`

Explanation

Compression of spring S=150-100=50
mm
`sumP=0` (since the force are in equilibrium)
`R_(2) cos 60^(@)-R_(M)cos 30^(@)=0`
`rArrR_(L)=1.732R_(M)`. . . .(1)

`R_(L)sin theta-P_(S)-W-R_(M)sin 30^(@)=0`
`R_(M)=70N R_(jL)=1.732=70=121.24N`