Question 160: Laws of Motion

Question

A light string passing over a smooth light pulley connects two blocks of masses $${m_1}$$ and $${m_2}$$ (vertically). If the acceleration of the system is $$g/8$$, then the ratio of the masses is

Accepted Answer

Assume that, mass m
1
is greater than mass m
2
, so the heavier mass m
1
is accelerating downward and the lighter mass m
2
is accelerating upwards.
For mass $${m_1}$$ the equation will be
$${m_1}$$$$g-T=$$$${m_1}$$$$a$$
For mass $${m_2}$$ the equation will be
$$T-$$$${m_2}$$$$g=$$$${m_2}$$$$a$$
Adding those equations we get
$$a = {{\left( {{m_1} - {m_2}} ight)g} \over {{m_1} + {m_2}}}$$
$$	herefore$$ $${g \over 8} = {{\left( {{m_1} - {m_2}} ight)g} \over {{m_1} + {m_2}}}$$
$$ \Rightarrow {1 \over 8} = {{{{{m_1}} \over {{m_2}}} - 1} \over {{{{m_1}} \over {{m_2}}} + 1}}$$
$$ \Rightarrow$$ $${{{m_1}} \over {{m_2}}} + 1 =$$ $${8\left( {{{{m_1}} \over {{m_2}}} - 1} ight)}$$
$$ \Rightarrow$$ $${{{m_1}} \over {{m_2}}} = {9 \over 7}$$

Answer

$$8:1$$

Answer

$$9:7$$

Answer

$$4:3$$

Answer

$$5:3$$

Laws of Motion

A light string passing over a smooth light pulley connects two blocks of masses ${m_1} and {m_2} (vertically). If the acceleration of the system is g/8$, then the ratio of the masses is

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