Two-blocks-of-masses-M-and-2M-are-connected-to-each-other-through-a-light-spring-as-shown-in-figure-If-we-push-the-mass-M-with-a-force-F-which-cause-acceleration-a-in-mass-M-what-will-the-accelerati

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Question Number 18965 by Tinkutara last updated on 02/Aug/17

$$\mathrm{Two}\mathrm{blocks}\mathrm{of}\mathrm{masses}M\mathrm{and}2M\mathrm{are}$$$$\mathrm{connected}\mathrm{to}\mathrm{each}\mathrm{other}\mathrm{through}\mathrm{a}\mathrm{light}$$$$\mathrm{spring}\mathrm{as}\mathrm{shown}\mathrm{in}\mathrm{figure}.\mathrm{If}\mathrm{we}\mathrm{push}\mathrm{the}$$$$\mathrm{mass}M\mathrm{with}\mathrm{a}\mathrm{force}F\mathrm{which}\mathrm{cause}$$$$\mathrm{acceleration}\mathrm{a}\mathrm{in}\mathrm{mass}M,\mathrm{what}\mathrm{will}\mathrm{the}$$$$\mathrm{acceleration}\mathrm{in}2M?$$

Commented by Tinkutara last updated on 02/Aug/17

Commented by Tinkutara last updated on 03/Aug/17

$$\mathrm{But}\mathrm{in}\mathrm{options}\mathrm{it}\mathrm{is}\mathrm{in}\mathrm{terms}\mathrm{of}F,M\mathrm{and}a.$$

Commented by ajfour last updated on 02/Aug/17

$$\mathrm{initially}\mathrm{zero}.$$

Answered by ajfour last updated on 03/Aug/17

$$\mathrm{F}-\mathrm{kx}=\mathrm{Ma}$$$$\mathrm{kx}=2\mathrm{MA}$$$$\Rightarrow \mathrm{A}=\frac{\mathrm{kx}}{2\mathrm{M}}=\frac{\mathrm{F}-\mathrm{Ma}}{2\mathrm{M}}$$$$\mathrm{A}=\frac{\mathrm{F}}{2\mathrm{M}}-\frac{\mathrm{a}}{2}.$$$$\left(\mathrm{A}\mathrm{being}\mathrm{acceleration}\mathrm{of}2\mathrm{M}\right).$$

Commented by Tinkutara last updated on 03/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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