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

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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