Question

On the horizontal surface of a truck a block of mass of $1kg$ is placed ($\mu =0.6$ ) and truck is moving with the acceleration $5m/{{s}^{2}}$ then the frictional force on block will be:
$A.5N$
$B.6N$
$C.5.88N$
$D.8N$

Answer 1

Concept of pseudo force and frictional force will be used. We know that frictional force acts in the opposite direction to that of motion and opposes any relative motion between the surfaces. Pseudo force is that force which acts on all masses whose motion is described using a non inertial frame of reference.
Formula Used:
We are going to use the following formulae to solve the given problem:-
${{F}_{p}}=ma$ and ${{F}_{r.}}=\mu mg$

Complete step by step solution:
From the given problem we have the following parameters with us:-
Mass of block, $m=1kg$
Acceleration due to gravity, $g=10m/{{s}^{2}}$
Coefficient of friction, $\mu =0.6$.
Frictional force, ${{F}_{r}}$ is given as follows:-
${{F}_{r.}}=\mu mg$……………. $(i)$
Using the parameters in equation $(i)$ we get,
${{F}_{r}}=0.6\times 1\times 10$
$\Rightarrow {{F}_{r}}=6N$…………….. $(ii)$
For the movement the block has to overcome this frictional force of $6N$.
We also know that the truck is moving with the acceleration and hence, the pseudo force (${{F}_{p}}$ ) acts on the block because the truck has accelerated but the block is not accelerated. Pseudo force has been given as follows:-
${{F}_{p}}=ma$…………………… $(iii)$
Putting the values in $(ii)$ we get
${{F}_{p}}=1\times 5$
${{F}_{p}}=5N$…………….. $(iv)$
As we clearly see that this force is less than the frictional force and it will not be able to move the block. Therefore, an equal frictional force on the block which is opposite in direction of magnitude $5N$ will act on the block to keep the block in equilibrium.

Hence, option $(A)$ is correct.

Note:
We should take care of the fact that friction force always acts in direction opposite to the motion. Friction between two bodies when there is no relative motion is called static friction. A body needs to overcome the static friction in order to move. Kinetic friction and static friction are different types of friction.