Question

Planck's constant has the same dimensions as

• A. Angular momentum
• B. Linear momentum
• C. Work
• D. Coefficient of viscosity

Answer 1

The correct option is A

Angular momentum

Explanation for the correct option

In the case of option A,

1. Angular momentum$\left(\mathrm{L}\right)$ has the formula as $\mathrm{L}=\mathrm{nh}/2\mathrm{\pi }$,where $\mathrm{h}$ is the Planck's constant.
2. $\mathrm{nh}/2\mathrm{\pi }$ is a constant and can be neglected during dimension calculation.
3. Hence, Angular momentum has the same dimension as of Planck's constant i.e $[M{L}^2{T}^{-1}]$

Explanation for incorrect options

In the case of option B,

1. Linear momentum has formula $p=mv$,where $m$is mass of an object and $v$ is the velocity.
2. Therefore dimensions of linear momentum is ${\mathrm{MLT}}^{-1}$.

In the case of option C,

1. Work has the formula $W=Fs$ where , $F$is the force applied and $s$is the displacement.
2. Therefore the dimension of work is $\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}$.

In the case of option D,

1. The coefficient of viscosity$\left(\eta \right)$ has the dimensional formula as ${\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}$.

Hence option A is the correct answer.