Question
The SI unit of energy is kg m2/sec2, that of speed v is m/s and that of acceleration a is m/s2.
Which of the formulae for kinetic energy given below can you rule out by dimensional arguments (m stands for mass of body):
(a) KE = m2 v3
(b) KE = 1/2 mv2
(c) KE = ma
(d) KE = 3 mv2
(e) KE = 1/2 mv2 + ma
Solution
The dimensional formula for KE is [M1L2T–2].
According to the principle of homogeneity of dimensional analysis, the dimensions of each term on both the sides of correct formula or equation will be the same.
The dimensions of quantity on R.H.S. of different equations are:
![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#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>](/application/zrc/images/qvar/PHEN11037436.png)
Since dimensional formula of the R.H.S. of (a), (c) and both the terms of R.H.S. of (e) are not same as that of L.H.S. i.e. [M1L2T2].
Therefore, the formulae (a), (c) and (e) are ruled out dimensionally.
