Question

A box of mass $100kg$ rests on the floor. A horizontal force $344N$ is applied to the box. Assume the coefficient of static friction between box and the floor is $0.5$ and coefficient of kinetic friction is $0.4$. Which of the following statements is true?
A) The box will accelerate across the floor at $0.5 ms^{-2}$.
B) The static friction force, which is the reaction force as guaranteed by Newton’s third law, will also have a magnitude of $344N$.
C) The box will slide across the floor at a constant speed of $0.5 m/s$.
D) The box will not move
E) None of the above

Answer 1

Hint
The coefficient of static friction helps to find out the amount of minimum force to be applied, to just take an acceleration in an object. Whereas kinetic friction constant helps in getting the amount of friction exhibited by the object during motion.
The force in static friction is calculated as static friction=$µ_s \times m \times g$ ,
Where $m$ is mass and $g$ is gravitational constant equivalent to $10ms^{-2}$.
Similarly, kinetic friction is calculated by Kinetic friction=$µ_k \times m \times g$.

Complete Step By Step Solution
Let’s begin with the given data. There is an object of mass $100kg$. which rests on the floor. The static friction will be equal to
Max Static Friction=$µ_s \times m \times g$
After putting the value, we get
Max Static friction=$0.5 \times 100 \times 10$
Max Static friction=$500 Newton(N)$
The amount of Force required to move the body is $500N$ and the amount of force applied is $344N$. Hence the object will have static friction equal to $344N$ and will not move. Now let’s check out the options, Option (A) describes the movement of the box with acceleration $5 {m}{s^{-2}}$ and thus it is incorrect.
Option (B) states that the static friction force will be $344N$ and it follows Newton's third law, hence is the incorrect Option.
In option (C), it states the box will slide with $5 m/s$ which is incorrect too.
In option (D), it stated that the box will not move.
Hence option (D) is the correct answer.

Note
The Kinetic friction force acts and is smaller then static frictional force. The net acceleration for the object in motion is the resultant force between actual force applied and kinetic frictional force.