In the column-II some arrangements with light string and frictionless and light pulley are shown. In string AB tension may be written as T = η m g . Some values of η is given in column-I, match the va

Question

In the column-II some arrangements with light string and frictionless and light pulley are shown. In string AB tension may be written as $T = η m g$ . Some values of $η$ is given in column-I, match the values with arrangements of column-II. All the surfaces shown are smooth.

List - I	List - II
(A) $η = \frac{1}{2}$	(P)
(B) $η = \frac{2}{3}$	(Q)
(C) $η = \frac{4}{3}$	(R)
	(S)

TestHub · Accepted Answer

(P) Two equal masses m: a = 2 g ​ , T = ma = 2 m g ​ ⇒ η = 2 1 ​ . (Q) From the free-body equations of the arrangement, tension in string AB: T = 3 2 m g ​ ⇒ η = 3 2 ​ . (R) Masses m and m/2 over pulley B: T ′ = m + 2 m ​ 2 ⋅ m ⋅ 2 m ​ ​ g = 3 2 m g ​ , support string 2 T ′ = 3 4 m g ​ ⇒ η = 3 4 ​ . (S) m on 30° smooth incline, 8m hanging: a = 9 m 8 m g − m g sin 3 0 ∘ ​ = 6 5 g ​ , T = 8 m ( g − a ) = 3 4 m g ​ ⇒ η = 3 4 ​ . Answer: (A) A → P, B → Q, C → RS

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