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 [AIEEE 2003]

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: A

Solution :

[a] 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.