Question

The force acting on a mass of $1\;g$ due to the gravitational pull on the earth is called $1\;gwt.$ One $\;gwt$ equals:
(A) $1\;N$
(B) $9.8\;N$
(C) $980\;dyne$
(D) None of these

Answer 1

Hint: It is given that the force acting on a body having a mass of $1\;g$ will be equal to $1\;gwt$. The weight of an object will be the result of the mass of the object as well as the acceleration due to gravity. The weight of the object will vary from place to place. Here we have to find the equivalent force of one $\;gwt$.

Complete Step by step solution:
The weight of an object is the product of its given mass and the acceleration due to the gravity of the earth. Hence we can write $1\;gwt$ as,
The mass of the object is given as $1\;g$
We know that the acceleration due to gravity is generally taken as $9.8m/{s^2}$
Putting these values into an equation, we can write,
$1gwt = 1g \times 9.8m/{s^2}$
We can write $1\;g$ as,$1g = \dfrac{1}{{1000}}kg$
Putting this in the above equation, we get
$1gwt = \dfrac{1}{{1000}} \times 9.8$
We know that force is the product of mass and acceleration, hence we can write
$1gwt = 0.001kg \times 9.8m/{s^2} = 0.0098N$
We know that the value of $1N = {10^5}dyne$
Substituting this value in the above equation, we get
$1gwt = 0.0098 \times {10^5}dyne = 980dyne$
Therefore, we can say that-
The correct answer is: Option (C): $980\;dyne$.

Note:
There are two types of masses. The inertial mass of a body is defined as the ratio of the force applied on the body to the acceleration produced on it. But gravitational mass is defined as the ratio of the weight of the body to the acceleration due to gravity. It is equal to the inertial mass. Thus we conclude that inertial and gravitational masses are the same for everybody in the universe.