JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Laws of Motion

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All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :

(A)g
(B) $\frac{g}{3}$ ✓ Correct
(C) $\frac{g}{2}$
(D) $\frac{g}{4}$

Answer: (B)

Solution

Let the acceleration of the 2 kg block be

2 a

and that of the 4 kg block be

a

(from the pulley constraint).

For the 4 kg block:

40 - 2 T = 4 a

For the 2 kg block:

T - 10 = 4 a

From the second equation,

T = 10 + 4 a

; substituting into the first,

40 - 2 (10 + 4 a) = 4 a \Rightarrow 20 = 12 a \Rightarrow a = \frac{5}{3}

.

The acceleration of the 2 kg block is

2 a = \frac{10}{3} = \frac{g}{3}

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option

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