question_answer

A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is

A)  both the scales read M kg each

B)  the scale of the lower one reads M kg and of the upper one zero

C)  the reading of the two scales can be anything but the sum of the readings will be M kg

D)  both the scales read M / 2 kg

Correct Answer: D

Solution :

The arrangement is shown in figure. Now draw the free body diagram of the spring balances and block. For equilibrium of block,                 \[{{T}_{1}}=Mg\] where \[{{T}_{1}}=\]Reading of\[{{S}_{2}}\] For equilibrium of\[{{S}_{2}},\,\,{{T}_{2}}={{T}_{1}}\] where   \[{{T}_{2}}=\]Reading of\[{{S}_{1}}\] For equilibrium of\[{{S}_{1}},\,\,{{T}_{2}}={{T}_{3}}\] Hence,                  \[{{T}_{1}}={{T}_{2}}=Mg\] So, both scales read\[M\,\,kg\].