Let's solve this problem step-by-step:
1. Understanding the Problem:
- We have a force of 4 kg wt.
- This force produces an acceleration of [tex]\(4 \, \text{m/s}^2\)[/tex] in a body.
- We need to find the mass ([tex]\(m\)[/tex]) of the body.
- The acceleration due to gravity ([tex]\(g\)[/tex]) is given as [tex]\(9.8 \, \text{m/s}^2\)[/tex].
2. Converting kg wt to Newtons:
- 1 kg wt is equal to the weight of a 1 kg mass under standard gravity ([tex]\(g = 9.8 \, \text{m/s}^2\)[/tex]).
- Therefore, 1 kg wt is equivalent to [tex]\(1 \times 9.8 = 9.8 \, \text{Newtons (N)}\)[/tex].
3. Calculate the force in Newtons:
- A force of 4 kg wt is:
[tex]\[
4 \, \text{kg wt} \times 9.8 \, \text{N/kg wt} = 39.2 \, \text{N}
\][/tex]
4. Apply Newton's Second Law of Motion:
- Newton's second law states that [tex]\(F = m \times a\)[/tex], where [tex]\(F\)[/tex] is the force, [tex]\(m\)[/tex] is the mass, and [tex]\(a\)[/tex] is the acceleration.
- Rearranging the formula to solve for [tex]\(m\)[/tex] (mass):
[tex]\[
m = \frac{F}{a}
\][/tex]
5. Substitute the given values:
- Force ([tex]\(F\)[/tex]) = 39.2 N
- Acceleration ([tex]\(a\)[/tex]) = 4 \, \text{m/s}^2
Thus:
[tex]\[
m = \frac{39.2 \, \text{N}}{4 \, \text{m/s}^2} = 9.8 \, \text{kg}
\][/tex]
6. Conclusion:
- The value of the mass [tex]\(m\)[/tex] is [tex]\(9.8 \, \text{kg}\)[/tex].
So, the mass of the body is [tex]\(9.8 \, \text{kg}\)[/tex].
