Motion Of Blocks When Connected With String MCQ

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Three identical blocks of masses 2kg each, are kept on smooth surface. The system is drawn by applying forces of 15N and 3N as shown in the figure. Determine the Tension T₁ (in N) in one string as shown in the figure.

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Concepts Covered - 1

Motion of blocks when connected with string

Two blocks connected with a string on smooth horizontal surface

Let accelereration of the blocks be 'a', and Tension in the string be T.

F.B.D of both blocks combined-

$\\ From\ F_{net}=M_{sys}a\\ F=(m_{1}+m_{2})a\\ \Rightarrow a=\frac{F}{m_{1}+m_{2}}\ ...(1)$

F.B.D of block of mass m₁-

$\\ From\ F_{net}=M_{sys}a\\ T=m_{1}a\\ From\ equation (1)\\ \Rightarrow T=\frac{m_{1}F}{m_{1}+m_{2}} \ ...(2)$

Three blocks connected with a string on smooth horizontal surface

Let accelereration of the blocks be 'a', tension in the string between m₁and m₂be T₁, and tension between m₂ and m₃ be T₂.

F.B.D of all the blocks combined-

$\\ From\ F_{net}=M_{sys}a\\ F=(m_{1}+m_{2}+m_{3})a\\ \Rightarrow a=\frac{F}{m_{1}+m_{2}+m_{3}} \ ...(1)$

F.B.D of block m_1-

F.B.D of m_3-

$\\ From\ F_{net}=M_{sys}a\\ F-T_{2}=m_{3}a\\ \Rightarrow T_{2}=\frac{(m_{1}+m_{2})F}{m_{1}+m_{2}+m_{3}}\ ...(3)$

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