Question

Choose the correct option based on the statements provided below:
1: Surface tension and spring constant have the same dimensions.
2: Both are equivalent to force per unit length

(a) 1 and 2 are correct and 2 is correct explanation of 1
(b) 1 and 2 are correct and 2 is not the correct explanation of 1
(c) 1 is true and 2 is false
(d) 1 is false and 2 is true

Answer 1

Hint: In this question use the concept that spring force is given as $F = kx$ where k is the spring constant and x is the spring length. Use this to get the basic dimension of spring force. Then use the basic definition of surface tension that is it is the force per unit length. This will help get the right answer.

Complete Step-by-Step solution:
As we know that the spring force acting on a stretched or compressed spring is given as
$ \Rightarrow F = kx$, where F = spring force, x = spring length and k = spring constant.
$ \Rightarrow k = \dfrac{F}{x}$ N/m = force per unit length of the spring.
On the other hand Surface tension, represented by the symbol T and is measured in force per unit length.
So surface tension T = force per unit length.
Therefore both statements are true and statement – 2 is the correct explanation of the statement – 1.
Hence option (B) is the correct answer.

Note – The spring force is the force which is extended by a spring either compressed or stretched upon an object that is attached to it. An object that compresses or stretches a spring is always acted upon by a force that restores the object to its rest or equilibrium position. Surface tension is the tension of the surface film or a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.