A block of mass m is connected with another block of mass 2m by a light spring. 2m is connected with a hanging mass 3m by an inextensible light string. At the time of release of block 3m, find tension in the string and acceleration of all the masses.


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Question Number 21388 by Tinkutara last updated on 22/Sep/17

$A block of mass m is connected with$ $another block of mass 2 m by a light$ $spring . 2 m is connected with a hanging$ $mass 3 m by an inextensible light string .$ $At the time of release of block 3 m, find$ $tension in the string and acceleration$ $of all the masses .$
Commented by Tinkutara last updated on 22/Sep/17

Commented by mrW1 last updated on 22/Sep/17

$since the string is inextensible,$ $‘ ‘ {2 m}^{″} and ‘ ‘ {3 m}^{″} have the same$ $velocity and acceleration .$ $let T = tension in the string$ $let a = acceleration of ‘ ‘ {2 m}^{″} and ‘ ‘ {3 m}^{″}$ $3 mg - T = 3 ma$ $T = 2 ma$ $\Rightarrow a = \frac{3}{5} g = 0 . 6 g$ $\Rightarrow T = \frac{6}{5} mg = 1 . 2 mg$ $the elongation of the spring is zero,$ $therefore the force in it is also zero .$ $\Rightarrow the acceleration of ‘ ‘ m^{″} is zero .$
Commented by Tinkutara last updated on 23/Sep/17

$Thank you very much Sir!$
Commented by mrW1 last updated on 23/Sep/17

$at t = 0 the displacement of ‘ ‘ {2 m}^{″} is$ $zero, therefore the force in the spring$ $between ‘ ‘ m^{″} and ‘ ‘ {2 m}^{″} is zero .$ $\Rightarrow acceleration of ‘ ‘ m^{″} is zero at t = 0 .$ $this is independent from which mass$ $it has .$
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