Two masses M₁ and M₂ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M₂ is twice that of M₁, the acceleration of the system is a₁. When the mass M₂ is thrice that of M₁, the acceleration of the system is a₂. The ratio (a₁)/(a₂) will be: (a) 1/3 (b) 2/3 (c) 3/2 (d) 1/2

Answer: (b). Atwood machine: a = ((M₂ - M₁)g)/(M₁ + M₂). M₂ = 2M₁: a₁ = (M₁ g)/(3M₁) = g/3 M₂ = 3M₁: a₂ = (2M₁ g)/(4M₁) = g/2 (a₁)/(a₂) = 2/3, so the answer is (b).

Two masses M₁ and M₂ are tied together at the two ends of a light… | JEE Main 2022 (26 Jul, Shift 2)

Q25JEE Main 2022 · 26 JUL · SHIFT 2Medium

Connected Bodies & Pulleys

Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_2$ is twice that of $M_1$ , the acceleration of the system is $a_1$ . When the mass $M_2$ is thrice that of $M_1$ , the acceleration of the system is $a_2$ . The ratio $\frac{a_1}{a_2}$ will be:

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Answer: (b)

Atwood machine: $a = \dfrac{(M_2 - M_1)g}{M_1 + M_2}$ .
$M_2 = 2M_1$ : $a_1 = \dfrac{M_1 g}{3M_1} = \dfrac{g}{3}$
$M_2 = 3M_1$ : $a_2 = \dfrac{2M_1 g}{4M_1} = \dfrac{g}{2}$
$\dfrac{a_1}{a_2} = \dfrac{2}{3}$ , so the answer is (b).

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