A sphere resting in a smooth V shaped groove and subjected to a spring force, is shown in the figure. The spring is compressed to a length of 100 mm from its free length of 150 mm. If the stiffness of spring $K = 2 N / mm$ . The contact reaction $R_{L}$ and $R_{M}$ at the points L and M respectively are

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Compression of spring S = 150 − 100 = 50 mm P = 0 (since the force are in equilibrium) ​ R 2 ​ cos 6 0 ∘ − R M ​ cos 3 0 ∘ = 0 ​ ⇒ R L ​ = 1.732 R M ​ … . ( 1 ) ​ R L ​ sin θ − P S ​ − W − R M ​ sin 3 0 ∘ = 0 ​ R M ​ = 70 N R L ​ = 1.732 × 70 = 121.24 N ​

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