JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Laws of Motion

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The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use

g = 10 m / s^{2}

)

(A)0.25 s
(B)0.4 s✓ Correct
(C)0.34 s
(D)0.2 s

Answer: (B)

Solution

The

8

kg block hangs from a movable pulley held by two string segments, while the

2

kg block hangs from the free end over the fixed pulley. With a single tension

T

throughout, the movable pulley and the

8

kg block descending with acceleration

a

give

8 g - 2 T = 8 a,

and the constraint makes the

2

kg block rise with acceleration

2 a

T - 2 g = 2 (2 a) .

Eliminating

T

gives

2 g - 4 a = 4 a

, so

a = \frac{g}{4} = 2.5

m/s

^{2}

. Starting from rest and falling

0.20

0.20 = \frac{1}{2} a t^{2} = \frac{1}{2} (2.5) t^{2} \Rightarrow t^{2} = 0.16,

so the

8

kg block reaches the ground in

0.4

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Single correct option

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JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Laws of Motion

Solution

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