Blocks of masses m , 2 m , 4 m and 8 m are ar | vedclass

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Question

All collisions are perfectly inelastic, so affer the final collision, all blocks are moving together. So let the final velocity be $v^{\prime},$ so on

Vedclass · Accepted Answer

$94$

Vedclass · Answer

All collisions are perfectly inelastic, so affer the final collision, all blocks are moving together. So let the final velocity be $v^{\prime},$ so on applying momentum conservation:

$mv =16 m v ^{\prime} \Rightarrow v ^{\prime}= v / 16$

Now initial energy $E _{1}=\frac{1}{2} mv ^{2}$

Final energy $: E _{ f }=\frac{1}{2} 	imes 16 m 	imes\left(\frac{ v }{16}ight)^{2}$

$\Rightarrow E _{ f }=\frac{1}{2} m \frac{ v ^{2}}{16}$

Energy loss : $E _{ i }- E _{ f }$

$\Rightarrow \frac{1}{2} mv ^{2}-\frac{1}{2} m \frac{ v ^{2}}{16}$

$\Rightarrow \frac{1}{2} mv ^{2}\left[1-\frac{1}{16}ight] \Rightarrow \frac{1}{2} mv ^{2}\left[\frac{15}{16}ight]$

$\% p=\frac{	ext { Energy loss }}{	ext { Original energy }} 	imes 100$

$=\frac{\frac{1}{2} mv ^{2}\left[\frac{15}{16}ight]}{\frac{1}{2} mv ^{2}} 	imes 100=93.75 \%$

$\Rightarrow$ Value of $P$ is close to $94$

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