Question

In the above figure, two boys A and B are shown applying force on a block. If the block moves towards the right, which one of the following statements is correct?

A.The magnitude of force applied by A is greater than that of B.
B.The magnitude of force applied by A is smaller than that of B.
C.The net force on the block is towards A.
D.The magnitude of force applied by A is equal to that of B.

Answer 1

You can start by discussing what vector quantities are. Then write down the equation for the net force on the box, i.e. ${F_T} = {F_A} - {F_B}$ . Use this equation and the information of the direction of movement of the box given in the problem to reach the solution.

Complete answer:
Before attempting the numerical calculations, let’s first discuss what a vector is?
A vector is a mathematical quantity that has both a magnitude (size) and a direction. To imagine what a vector is like, imagine asking someone for directions in an unknown area and they tell you, “Go $5km$ towards the West”. In this sentence, we see an example of a displacement vector, “ $5km$ ” is the magnitude of the displacement vector, and “towards the North” is the indicator of the direction of the displacement vector.
A vector quantity is different from a scalar quantity in the fact that a scalar quantity has only magnitude, but a vector quantity possesses both direction and magnitude. Unlike scalar quantities, vector quantities cannot undergo any mathematical operation, instead they undergo Dot product and Cross product.
Some examples of vectors are – Displacement, Force, Acceleration, Velocity, Momentum, etc.
To solve this particular problem we have to see what the net force on the object is.
Let the net force on the block be ${F_T}$ , the force applied by boy A be ${F_A}$ and the force applied by boy B be ${F_B}$ .
${F_T} = {F_A} - {F_B}$ (Assuming that the direction of ${F_A}$ is positive)
Now, since the block is moving towards the right i.e, in the same direction as ${F_A}$ . We can safely conclude that ${F_A} > {F_B}$ .

Hence, option A is the correct choice.

Note:
Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. Acceleration of an object depends on two things, force and mass.