JEE Main 20204 SeptemberMorning Shift

JEE Main 2020 · 4 September · Morning Shift · Physics · Center of Mass, Momentum and Collision

Blocks of masses m, 2m, 4m and 8m are arranged in a line of a...

Blocks of masses

\text{m}, 2\text{m}, 4\text{m}

and

8\text{m}

are arranged in a line of a frictionless floor. Another block of mass

m

, moving with speed

υ

along the same line (see figure) collides with mass

m

in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass

8\text{m}

starts moving the total energy loss is

\text{p%}

of the original energy. Value of ‘

\text{p}

’ is close to:
Blocks of masses m, 2m, 4m and 8m are arranged in a line of a frictionless floor. Another block of mass m , moving with

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B. $94$

Blocks of masses m, 2m, 4m and 8m are arranged in a line of a frictionless floor. Another block of mass m , moving with

Inelastic collision

$mv = 16{mv}^{1}$

$\Delta Kloss = \dfrac{1}{2}{mv}^{2} - \dfrac{1}{2}\left(16M\right){\left(\dfrac{v}{16}\right)}^{2}$

$= \dfrac{1}{2}{mv}^{2} - \dfrac{1}{2}M\dfrac{{v}^{2}}{16}$

$= \dfrac{1}{2}{mv}^{2}\left(\dfrac{15}{16}\right)$

$% \Delta Kloss = \dfrac{\dfrac{1}{2}{mv}^{2}\left(\dfrac{15}{16}\right)}{\dfrac{1}{2}{MV}^{2}} \times 100 = \dfrac{15}{16} \times 100 = 93 .75 %$