Question
Read each statement below carefully and state, with reasons and examples, if it is true or false:
A scalar quantity is one that
(a) is conserved in a process.
(b) can never take negative values.
(c) must be dimensionless.
(d) does not vary from one point to another in space.
(e) has the same value for observers with different orientations of axes.
Solution
(a) False - When we carry out the adiabatic process, the scalar quantity temperature does not conserve.
In inelastic collisions, the K.E. (scalar quantity) does not conserve.
(b) False - scalar quantity can have negative value e.g.![<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)
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.
If the angle between![<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)
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is greater than 
then W will be negative e.g. work done by gravitational force when body is raised upward is negative.
(c) False - Scalar quantity may have dimensions, e.g. Dimensional formula of work is [M1L2T-2].
(d) False - Temperature is a scalar quantity and it changes as we go higher, the gravitational potential is a scalar quantity and it varies with the height.
(e) True.
In inelastic collisions, the K.E. (scalar quantity) does not conserve.
(b) False - scalar quantity can have negative value e.g.
.If the angle between
is greater than then W will be negative e.g. work done by gravitational force when body is raised upward is negative.(c) False - Scalar quantity may have dimensions, e.g. Dimensional formula of work is [M1L2T-2].
(d) False - Temperature is a scalar quantity and it changes as we go higher, the gravitational potential is a scalar quantity and it varies with the height.
(e) True.
