Question

State whether true or false: The SI unit of gravitational units of work is g wt-m is:
A) True
B) False

Answer 1

Hint: When a force moves a body through one unit distance in the direction of force work is said to be done. Similarly, if a gravitational force moves a body through one unit distance in the direction of force work is said to be done. Thus, using the above definition we will derive the unit of Gravitational work.

Complete solution:
Let us define work, its units and Gravitational work and its units.
Unit work is the amount of work done when a unit force displaces a body through a unit distance in the direction of the force. Therefore units of work will depend on the units of force and distance.
Unit of work is:
$ \Rightarrow 1newton \times 1metre$
$ \Rightarrow 1kgwt \times 1m$ (Newton is the unit of force and meter is the unit of distance)
Similarly,
Gravitational unit of work, work is said to be one gravitational unit if a gravitational unit of force moves a body through unit distance in the direction of force.
In cgs system unit of gravitational unit of work unit of work is:
One gram centimeter of work is said to be done when a force of one gram weight displaces a body through one centimeter in its own direction.
$1 dyne cm = 1 g wt \times 1 cm$
In SI unit Gravitational unit of work is:
One kilogram meter of work is said to be done when a force of one kilogram weight displaces a body through one meter in its own direction .
$1 Kgwt m = 10^3 g wt \times m$
Thus, the SI unit of gravitational unit of work is not $Kg wt m$; the statement given in the question is false.

Note: SI unit of work is joule and in cgs system work has unit called erg. one erg of work is said to be done when a force of one dyne displaces a body through one centimeter in its own direction. 1 erg is equal to 1 dyne multiplied by 1 centimeter, thus 1 erg is known as dyne centimeter.