Question

1 kg-f is equal to.
A. 98 N
B. 980 N
C. 9.8 N
D. 0.98 N

Answer 1

Hint: 1 kg-f is the force exerted on 1 kg mass of the body kept in the gravitational field of acceleration due to gravity g. Use the formula for gravitational force to determine 1 kg-f. The value of acceleration due to gravity is \[9.8\,{\text{m/}}{{\text{s}}^2}\].

Formula used:
Gravitational force, \[F = mg\]
Here, m is the mass and g is the acceleration due to gravity.

Complete step by step answer:
1 kg-f is the force exerted on 1 kg mass of the body kept in the gravitational field of acceleration due to gravity g. We know the gravitational force exerted on the body of mass m is expressed as,
\[F = mg\]
Here, g is the acceleration due to gravity.

Substituting 1 kg for m and \[9.8\,{\text{m/}}{{\text{s}}^2}\] for g in the above equation, we get,
\[F = \left( {1\,{\text{kg}}} \right)\left( {9.8\,{\text{m/}}{{\text{s}}^2}} \right)\]
\[ \Rightarrow F = 9.8\,{\text{N}}\]

Therefore, 1 kg-of force is equal to 9.8 N. So, the correct answer is option C.

Additional information:
According to Newton’s second law of motion, the force exerted on the body is the product of mass of the body and the acceleration produced in the body due to this force. It is expressed as,
\[F = ma\]
Here, m is the mass and a is the acceleration.

The body in the rest position is acted by the gravitational force. The acceleration produced by this force is the acceleration due to gravity. Therefore, we can express the gravitational force as,
\[F = mg\]
The S.I unit of force is newton and the C.G.S unit of force is dyne.

Note: We have assumed the acceleration due to gravity is \[9.8\,{\text{m/}}{{\text{s}}^2}\]. But the acceleration due to gravity changes place to place. It changes as we move from the pole to the equator of the earth. However, the change is very small, therefore we neglect this effect. Note that kg is the unit of mass and not the unit of weight. The weight itself is the gravitational force.