A light string passing over a smooth light pulley connects two blocks of masses and (where ). If the acceleration of the system is , then the ratio of the masses is:

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Q.
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (where $m_{2} > m_{1}$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_{1}}{m_{2}}$ is: [2024]

1 $\frac{\sqrt{3} + 1}{\sqrt{2} - 1}$

2 $\frac{1 + \sqrt{5}}{\sqrt{2} - 1}$

3 $\frac{1 + \sqrt{5}}{\sqrt{5} - 1}$

4 $\frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

Ans.
(4)

$a = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g \Rightarrow \frac{g}{\sqrt{2}} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g$

$(m_{1} + m_{2}) = \sqrt{2} m_{2} - \sqrt{2} m_{1}$

$\Rightarrow \frac{m_{1}}{m_{2}} = (\frac{\sqrt{2} - 1}{\sqrt{2} + 1})$

Solution

Q.
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (where $m_{2} > m_{1}$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_{1}}{m_{2}}$ is: [2024]

1 $\frac{\sqrt{3} + 1}{\sqrt{2} - 1}$

2 $\frac{1 + \sqrt{5}}{\sqrt{2} - 1}$

3 $\frac{1 + \sqrt{5}}{\sqrt{5} - 1}$

4 $\frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

Ans.
(4)

$a = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g \Rightarrow \frac{g}{\sqrt{2}} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g$

$(m_{1} + m_{2}) = \sqrt{2} m_{2} - \sqrt{2} m_{1}$

$\Rightarrow \frac{m_{1}}{m_{2}} = (\frac{\sqrt{2} - 1}{\sqrt{2} + 1})$

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Solution

Q. A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2>m1). If the acceleration of the system is g2, then the ratio of the masses m1m2 is: [2024]

1 3+12-1

2 1+52-1

3 1+55-1

4 2-12+1

Ans. (4) a=(m2-m1m1+m2)g⇒g2=(m2-m1m1+m2)g (m1+m2)=2m2-2m1 ⇒m1m2=(2-12+1)

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Q.
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (where $m_{2} > m_{1}$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_{1}}{m_{2}}$ is: [2024]

1 $\frac{\sqrt{3} + 1}{\sqrt{2} - 1}$

2 $\frac{1 + \sqrt{5}}{\sqrt{2} - 1}$

3 $\frac{1 + \sqrt{5}}{\sqrt{5} - 1}$

4 $\frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

Ans.
(4)

$a = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g \Rightarrow \frac{g}{\sqrt{2}} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g$

$(m_{1} + m_{2}) = \sqrt{2} m_{2} - \sqrt{2} m_{1}$

$\Rightarrow \frac{m_{1}}{m_{2}} = (\frac{\sqrt{2} - 1}{\sqrt{2} + 1})$