Question

Dyne-sec the unit of:
A. Momentum
B. Force
C. Work
D. Angular momentum

Answer 1

Hint: Dyne and second are the units of force and time respectively in the cgs system (centimetre-gram-second system of units).The cgs system is the variant of the metric system which is the SI system. In cgs the system the centimetre is the unit length, gram is the unit of mass, second as the unit of time.

Complete answer:
Dyne can be defined as the force required to accelerate mass of one gram at the rate of one centimetre per second squared ( $1$ dyne=$1$$gcm/{{s}^{2}}$). Therefore, Dyne-sec will be$1gcm/{{s}^{2}}$.

The unit of momentum will be the product of units of mass and velocity, which implies momentum is in gram centimetre per second ( g.cm/s). Erg is the cgs unit of work where one erg= $1$g cm square/ second square. It can also be defined as the force of $1$ dyne on a one centimetre distance.
$\text{Force}={{M}^{1}}{{L}^{1}}{{T}^{-2}} \\
\Rightarrow \text{Momentum}={{M}^{1}}{{L}^{1}}{{T}^{-1}} \\
\Rightarrow \text{Energy}=M{{L}^{2}}{{T}^{-2}} \\ $
$\therefore \text{Dyne-sec} ={{M}^{1}}{{L}^{2}}{{T}^{-2}}.{{T}^{1}}={{M}^{1}}{{L}^{1}}{{T}^{-1}}$
From the above mentioned points it's clear that the dyne-sec is the unit of momentum.

Hence options A is correct.

Note:In SI unit system: the meter (m), the kilogram (kg), the second (s). Whereas in the cgs system; the centimetre (cm), gram(g), second (s). The dyne per centimeter is the unit used for measuring surface tension.The SI unit of force is Newton. Newtom can be defined as the force required to provide a mass of one kg with an acceleration of one metre per second per second.