# If a spring has a period $T$, and is cut into the $n$ equal parts, then the period of each part will be:

A. $T\sqrt n $

B. $\dfrac{T}{{\sqrt n }}$

C. $nT$

D. $T$

Last updated date: 21st Mar 2023

•

Total views: 181.2k

•

Views today: 4.59k

Answer

Verified

181.2k+ views

**Hint:**The spring constant is always in the linear range. At the lower gravity, the period did not change, The system’s equilibrium position gets different. Hence the period fully depends on the spring constant and mass of the object.

**Complete step by step solution:**

The hooke's law execute a simple harmonic motion as follows

The period $T$ , mass $m$ , and spring of spring constant \[K\] is given by the equation as follows,

$T = 2\pi \sqrt {\dfrac{m}{k}} $ ………(1)

After the spring is cut into four equal parts, let \[K\] be the spring constant of little spring. Hence all parts are equal we resume all small springs following Hooke's Law and have equal spring constant.

Where,

\[K\] is known as the proportionality constant and which is also called a spring constant. The spring constant \[K\] depends on the factors that are listed below,

Nature of the material of the spring,

Cross-Sectional Area of the spring,

Length of the spring.

For a spring,

$T = 2\pi \sqrt {\dfrac{m}{k}} $

For every piece of spring, the constant is $nk$

$T' = 2\pi \sqrt {\dfrac{m}{{nk}}} $

Rearrange the above equation and simplify the equation we get,

$T' = 2\pi \sqrt {\dfrac{m}{k} \times } \dfrac{1}{{\sqrt n }}$

Hence the period of each part is, $T' = \dfrac{T}{{\sqrt n }}$

**So, the correct answer is, Option (B)**

**Note:**

The spring constant and mass help to determine the period.

The equilibrium position of the system is determined by the gravitational force.

The equilibrium position does not depend on gravity.

Recently Updated Pages

Which element possesses the biggest atomic radii A class 11 chemistry JEE_Main

The highly efficient method of obtaining beryllium class 11 chemistry JEE_Main

Which of the following sulphates has the highest solubility class 11 chemistry JEE_Main

Amongst the metal Be Mg Ca and Sr of group 2 of the class 11 chemistry JEE_Main

Which of the following metals is present in the greencolored class 11 chemistry JEE_Main

To prevent magnesium from oxidation in the electrolytic class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE