Question

Kinetic energy of a comet moving in space is given by $k=\frac{\alpha m}{s^2}$ (where m is the mass of comet, and s is the distance travelled by comet. Determine dimensions of $\alpha .$

• A. $L^4{T}^{-2}$
• B. $L^2{T}^{-1}$
• C. $L{T}^{-2}$
• D. $L^2{T}^{-2}$

Answer 1

The correct option is A $L^4{T}^{-2}$

$\left[KE\right]=\left[M{L}^2{T}^{-2}\right]=\frac{\alpha \left[M\right]}{\left[L^2\right]}$
$\frac{M{L}^4{T}^{-2}}{M}=\alpha$
$\left[\alpha \right]=\left[L^4{T}^{-2}\right]$