question_answer

Two masses \[{{m}_{1}}\] and \[{{m}_{2}}\] which are connected with a light string, are placed over a frictionless pulley. This set up is placed over a weighing machine, as shown. Three combination of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are used, in first case \[{{m}_{1}}=6\,kg\] and \[{{m}_{2}}=2\,kg,\] in second case  \[{{m}_{1}}=5\,kg\] and \[{{m}_{2}}=3\,kg\] and in third case \[{{m}_{1}}=4\,kg\] and \[{{m}_{2}}=4\,kg\]. Masses are held stationary initially and then released. If the readings of the weighing machine after the release in three cases are\[{{W}_{1}},\,{{W}_{2}}\] and \[{{W}_{3}}\] respectively then:

A) \[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\]

B) \[{{W}_{1}}<{{W}_{2}}<{{W}_{3}}\]

C) \[{{W}_{1}}={{W}_{2}}={{W}_{3}}\]

D) \[{{W}_{1}}={{W}_{2}}<{{W}_{3}}\]

Correct Answer: B

Solution :

[b] Reading of the weighing machine \[=2T+\] weight of the machine. As weight of the machine is constant. \[T=\frac{2{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] So reading is maximum for the case \[{{m}_{1}}{{m}_{2}}\] is maximum as \[{{m}_{1}}{{m}_{2}}\] in all cases is same.