Two masses m and M are attached with strings as shown in the figure. For the system to be in equilibrium, we must have

Question

Two masses m and M are attached with strings as shown in the figure. For the system to be in equilibrium, we must have, tan θ = 1 + 2 M m, tan θ = 1 - 2 m M, tan θ = 1 - M 2 m, tan θ = 1 + m 2 M

MARKS App · Accepted Answer

mg = 2 Tsin 45 ° ⇒ mg = 2 T T 1 cos θ = T cos 4 5 ∘ ⇒ T 1 cos θ = T 2 = mg 2 ...(i) Further, Mg + T cos 4 5 ∘ = T 1 sin θ ∵ T = mg 2 ⇒ T 1 sin θ = Mg + mg 2 1 2 ...(ii) ⇒ tan θ = Mg + mg 2 mg 2 = 1 + 2 M m {dividing Eq. (ii) by Eq. (i)}

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