Answer :
To solve the problem of finding the magnitude of the horizontal force causing the motion of a body with mass [tex]m[/tex] tons, we need to analyze the given information step-by-step.
Given:
- The body has a mass [tex]m[/tex] tons. Note that [tex]1[/tex] ton is equal to [tex]1000[/tex] kg.
- There is a resistance force acting on the body. The magnitude of this resistance is given as 3 kg for each kg of the body’s mass.
First, we convert the mass from tons to kilograms. Since 1 ton equals 1000 kg:
[tex]m \text{ tons} = m \times 1000 \text{ kg}[/tex]
Resistance Force:
For each kilogram, the resistance is 3, which means:
- Total resistance force is [tex]3 \times ( ext{mass in kg})[/tex].
- Therefore, the total resistance on the body is:
[tex]3 \times (m \times 1000) = 3000m[/tex]
Force for Uniform Motion:
In order for the body to move with a uniform speed on a horizontal plane, the net force acting on it must be zero according to Newton’s First Law of Motion. This requires the applied force to exactly counteract the resistance force.
- Therefore, the magnitude of the horizontal force required to keep the body moving at a steady speed is the same as the resistance force.
So, the required horizontal force is:
[tex]3000m[/tex]
Conclusion:
The correct choice to keep the body moving with uniform speed is option 4) [tex]3000m[/tex].
