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Work, Energy And Power

Question
CBSEENPH11017292

A body of mass m1 moving with velocity u collides with a body of mass m2 at rest. Show that energy transfer in head-on elastic collision is maximum if m1 = m2.

Solution
The fractional energy transferred to target in head-on elastic collision when target is at rest is, 
space space space space space space space space space space space space space space space space straight K subscript 2 over straight K equals fraction numerator 4 straight m subscript 1 straight m subscript 2 over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis squared end fraction 
Let straight m subscript 2 equals nm subscript 1 
Therefore, 
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#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre> 
rightwards double arrow  straight K subscript 2 equals fraction numerator 4 straight n over denominator left parenthesis 1 plus straight n right parenthesis squared end fraction straight K 
The energy transfer is maximum if  dK subscript 2 over dn equals 0 
That is, 
                            straight d over dn open parentheses fraction numerator 4 straight n over denominator left parenthesis 1 plus straight n right parenthesis squared end fraction close parentheses equals 0 
rightwards double arrow  fraction numerator left parenthesis 1 plus straight n right parenthesis squared begin display style fraction numerator straight d left parenthesis 4 straight n right parenthesis over denominator dn end fraction end style minus 4 straight n begin display style fraction numerator straight d left parenthesis 1 plus straight n right parenthesis squared over denominator dn end fraction end style over denominator left parenthesis 1 plus straight n right parenthesis to the power of 4 end fraction equals 0 
rightwards double arrow            left parenthesis 1 plus straight n right parenthesis squared left parenthesis 4 right parenthesis minus 4 straight n left square bracket 2 left parenthesis 1 plus straight n right parenthesis right square bracket equals 0 
We have,  n = 1  
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#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre> 
Hence the result.