Question

A block of mass 10kg, moving with acceleration $2m/{s^2}$ on a horizontal rough surface is shown in figure. The value of coefficient of kinetic friction is

A) $0.2$
B) $0.4$
C) $0.5$
D) $0.1$

Answer 1

To find the solution of the given question we will recreate the given diagram for better understanding and find the forces acting on the given block. Then, solve the question by balancing the forces acting on the block.

Formula used:
$F = ma$

Complete answer:

From the figure we can see that, frictional force ‘${f_r}$ ’ is acting opposite to the force on the block, normal force ‘N’ is acting upwards and ‘mg’ acting downwards.
According to the figure, the normal force and the force exerted by the weight of the body gets balanced. Both of them are balanced forces. The force where two equal forces acting in opposite directions is defined as a balanced force.
$N = mg$ -- (i)
Friction is given as, ${f_r} = \mu N = \mu mg$
Equations of motion are the mathematical formulas which describe the position, velocity, or acceleration of a body relative to a given frame of reference.
Applying equation of motion, we will get,
$\Rightarrow F - {f_r} = ma$
Substituting the given values of mass of the body ‘m’, acceleration of the block ‘a’ and force ‘F’ acting on it, we get,
Here, we will take the value of ‘g’ as $g = 9.8$.
\eqalign{ & \Rightarrow 40 - \mu mg = ma \cr & \Rightarrow 40 - \mu \times 10 \times 9.8 = 10 \times 2 \cr & \Rightarrow 40 - 20 = 98\mu \cr & \Rightarrow \mu = \dfrac{{20}}{{98}} = \dfrac{{10}}{{48}} \cong 0.2 \cr}

So, the correct answer is “Option A”.

Note:
Normal force is also known as the contact force. It is defined as the force that the surface exerts to prevent objects from passing through each other. Weight of an object is the force of gravity on the object and is defined as the mass times the acceleration of the gravity. i.e. $w = mg$. Frictional force is defined as a force resisting the relative motion of solid surfaces, fluid layers and objects sliding against each other.