Question

Kinetic energy has the following dimensions:

• A. $[{\mathrm{M}}^2{\mathrm{L}}^2\mathrm{T}]$
• B. $[{\mathrm{ML}}^2\mathrm{T}]$
• C. $[{\mathrm{ML}}^2{\mathrm{T}}^{-2}]$
• D. $[{\mathrm{ML}}^2{\mathrm{T}}^{-1}]$

Answer 1

The correct option is C

$[{\mathrm{ML}}^2{\mathrm{T}}^{-2}]$

1. Kinetic energy is the type of energy that an object or particle has as a result of its motion.
2. The formula for the kinetic energy is written as:
   $Kineticenergy=\frac{1}{2}m{v}^2$ Where, $m$ is the mass of the particle, $v$ is the velocity of the particle.
3. The dimension of mass is $\left[\mathrm{M}\right]$.
4. The dimension of velocity is $\left[{\mathrm{LT}}^{-1}\right]$.
5. The dimension of kinetic energy is given as-

$\begin{array}{rcl}Kineticenergy& =& \mathrm{M}{\left[{\mathrm{LT}}^{-1}\right]}^2\\ & =& [{\mathrm{ML}}^2{\mathrm{T}}^{-2}]\end{array}$

Hence, option C is the correct answer.