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  4. Three blocks of masses m1,m2 and m3 are connected by massless string as shown kept on a frictionless table. They are pulled with a force T3=40N. If m1=10 kg,m2=6 kg and m3=4 text kg, the tension T2 will be:

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Q. Three blocks of masses $ {{m}_{1}},{{m}_{2}} $ and $ {{m}_{3}} $ are connected by massless string as shown kept on a frictionless table.
They are pulled with a force $ {{T}_{3}}=40N. $ If $ {{m}_{1}}=10\,kg,{{m}_{2}}=6\,kg $ and $ {{m}_{3}}=4\text{ }kg, $ the tension $ {{T}_{2}} $ will be:Physics Question Image

KEAMKEAM 2006

Solution:

Common acceleration
$ a=\frac{F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}} $
$ a=\frac{40}{10+6+4}=2\,m/{{s}^{2}} $
Equation of motion of $ {{m}_{3}} $ is $ {{T}_{3}}-{{T}_{2}}={{m}_{3}}a $
$ 40-{{T}_{2}}=4\times 2 $
$ \Rightarrow $ $ {{T}_{2}}=32N $