Question

A block of weight W is held against a vertical wall by applying a horizontal force F. The minimum value of F needed to hold the block is
A. Less than W
B. Equal to W
C. Greater or equal W
D. Data is insufficient.

Answer 1

Hint: The minimum force required to hold the block in contact with a wall is provided by the reaction force of the wall. The frictional force is equal to the product of coefficient of friction and normal reaction force.

Complete step by step answer:
When a block of weight W is held against a vertical wall by applying a horizontal force F which means the value of applied force should be greater than or equal to the reaction force applied by the wall because if the value of applied force is less than the reaction force applied by the wall on the block, the block would have felled down. This force which is acting perpendicular to the two surfaces in contact with each other i.e., the force applied by the wall on the block is known as normal reaction force.
This normal reaction force (N) is provided by the frictional force between the wall and block i.e., the required frictional force = $\mu N$where μ is known as coefficient of friction.
The force required to hold the block in place should be greater than or equal to the weight of the block i.e., $\mu N \geqslant W$
$\mu F \geqslant W$ [ As the applied force is equal to the Normal reaction force in a balanced condition]
$F \geqslant \dfrac{W}{\mu }$
Hence, we can say that the force needed to keep the block held against the wall is greater than or equal to W as the value of μ is either smaller or equal to 1.
The minimum force required is equal to W when the value of $\mu $ is 1.

So, the correct answer is “Option B”.

Note:
As a block is held against a vertical wall by applying some force. So, all the force acting on a block is in a balanced state. Hence, the applied force is equal to the normal reaction force and frictional force is equal to the weight.