A) \[8:1\]
B) \[9:7\]
C) \[4:3\]
D) \[5:3\]
Correct Answer: B
Solution :
As the string is inextensible, both masses have the same acceleration a. Also, the pulley is massless and frictionless, hence the tension at both ends of the string is the same. Suppose, the mass, \[{{m}_{2}}\] is greater than mass \[{{m}_{1}}\], so the heavier mass is accelerated downward and the lighter mass, \[{{m}_{2}}\] is accelerated upwards, Therefore, by Newton's 2nd law, \[T-{{m}_{1}}g={{m}_{1}}a\] ... (i) \[{{m}_{2}}g-T={{m}_{2}}a\] ... (ii) After solving Eqs. (i) and (ii), \[a=\frac{({{m}_{2}}(1-{{m}_{1}}/{{m}_{2\grave{\ }}})}{({{m}_{1}}+{{m}_{2}})}.g=\frac{g}{8}\] (given) So \[\frac{g}{8}=\frac{{{m}_{2}}(1-{{m}_{1}}/{{m}_{2}})}{{{m}_{2}}(1-{{m}_{1}}/{{m}_{2}})}.g\] .... (iii) Let \[\frac{{{m}_{1}}}{{{m}_{2}}}=x\] Thus, Eq. (iii) becomes \[\frac{1-x}{1+x}=\frac{1}{8}\] or \[x=\frac{7}{9}\] or \[\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{9}{7}\] So, the ratio of the masses is \[9:7\].You need to login to perform this action.
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