Question

1kgwt is equal to
A.) $980000\text{ dynes}$
B.) $9.80\text{ dynes}$
C.) $98\text{ dynes}$
D.) None of these

Answer 1

Hint: Kilogram weight is used to define the force of gravity acting on a mass ‘m’. Any body placed on the surface of the earth will have a force of gravity acting on it. So, when a body of mass m is placed on the surface of the earth it will experience a force which is the product of the mass of the body and the acceleration due to gravity (g).

Complete step by step answer:
We all know that a body placed on the surface of the earth will experience a force of gravity due to the earth’s gravitational field. So suppose we have a body of mass ‘m’ on the surface of the earth, this mass will experience a force of gravity given by the product of the mass of the body and the acceleration due to gravity (g). We usually call this the weight of the body. It can also be expressed as the kilogram weight of a mass ‘m’.

So in our problem, $1kgwt$ is given, which is the force of gravity acting on a body of mass of $1kg$. So, we can write it as,

$1kgwt=1\times 9.8=9.8N$

So, the $1kgwt$ is equivalent to 9.8 N. But, in the options, the answers are given in dynes.
Dyne is the unit of force in the C.G.S system. Newton and the dyne are related by the relation,
$1Newton={{10}^{5}}Dyne$.

So 9.8 N in dynes is $9.8\times {{10}^{5}}Dynes$ which is 980000 Dynes.

So, the answer to the question is the option(A).

Note: So, the dimensional formula for kilogram weight is the same as that of force which is $\left[ ML{{T}^{-2}} \right]$.
1 kgwt is the force that should be applied to a body of 1 kg to give an acceleration of $9.8m/{{s}^{2}}$ to the body.
The C.G.S unit of mass is grams and for length is centimetre (cm).