Boxes of masses 2, {kg} and 8, {kg} are connected by a massless string passing over smooth pulleys.

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4-1.Newton's 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 $\left.{g}=10\, {m} / {s}^{2}\right)$ (in ${s}$)

A

$0.34$

B

$0.2$

C

$0.25$

D

$0.4$

(JEE MAIN-2021)

Solution

$\left({m}_{1} {g}-2 {T}\right)={m}_{1} {a}…..(1)$

${T}-{m}_{2} {g}={m}_{2}(2 {a})$

$2 {T}-2 {m}_{2} {g}=4 {m}_{2} {a}…..(2)$

${m}_{1} {g}-2 {m}_{2} {g}=\left({m}_{1}+4 {m}_{2}\right) {a}$

${S}=\frac{1}{2} {at}^{2}$

$\frac{0.2 \times 2 \times 4}{10}={t}^{2}$

${t}=0.4\, {sec}$

Standard 11

Physics

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