Question

A 1 kg block is pushed against a wall by a force F= 75N as shown below. The coefficient of friction is 0.25. The magnitude of acceleration of the block is

               

A. 10$m/{s^2}$
B. 20$m/{s^2}$
C. 5$m/{s^2}$
D. none

Answer 1

Hint: In this question, first of all we will draw the free body diagram of the block indicating all the forces acting on the body. Then we calculate the magnitude of friction force using the given data of coefficient of friction and compare it with the gravitational force to get the acceleration.

Complete answer:
In the question, we have a body which is held against a wall by a force of 75N.
The coefficient of friction of the wall is $\mu $ =0.25.
And we have to find the acceleration of the body.
To calculate the acceleration of the block, first we draw a free body diagram(FBD) of the block indicating all the forces and then calculate net force acting on the block to get the net acceleration.

The FBD of the block is shown below:

The mass of the block = m= 1kg.
$\therefore $ Gravitational force on block = mg = 1$ \times $ 10= 10N
The pushed forced acting on the block is = F= 75N
Due to the wall the net acceleration of the body in horizontal direction is zero. Therefore, the wall will apply a normal force on the block in the opposite direction of F.
$\therefore $Normal force = N = 75N.
We know that the magnitude of friction force is given as:
f=$\mu $N
Putting the values in above equation, we get:
f= 0.25$ \times $75=18.75N.
$\because $ The magnitude of friction force is more than gravitational force.
So, in the vertical direction, there will be no motion of the block.
$\therefore $ The acceleration of the block in both horizontal and vertical direction is zero.
So, the block will not move i.e. a=0.

So, the correct answer is “Option D”.

Note:
In this question, you should first recognize the different forces acting on the block and then draw the free body diagram. The force due to friction always acts in the opposite direction of the motion of the body. The force due to gravity of earth always acts in downward direction.