A 100 g body hung on a spring, which elongates the spring by 4 cm. When a certain object is hung on the spring and set vibrating, its period is 0.568 s. What is the mass of the object pulling the spring? (Ans: 0.20 kg)


Data Given:

Mass of the body = m₁ = 100 g = 0.1 kg

Elongation = x = 4 cm = 0.04 m

Time period  = T = 0.568 s

Value of acceleration due to gravity = g = 9.8 m s⁻²



To Find:

Mass of the object hanged = m₂ = ?


Solution:


Here we will find the spring constant by using the Hook's law from given data for body of mass m₁ attached to spring

F = Kx

or

mg = Kx

or

K = `\frac {mg}{x}`

by putting values

K = `\frac {0.1 kg ｘ9.8 m s⁻² }{0.04 m}`

K = 24.5 N m⁻¹


Now using the formula for Time Period of mass attached to spring for object of mass m₂ 

T = 2Ï€ `\sqrt frac{m_2}{K}`

To separate the m₂ from this formula we will take square both side and by simplifying we get

m₂ = `\frac {T^2 K}{(2Ï€)^2}`

by putting values

m₂ = `\frac {(0.568 s)^2 ｘ 24.5 N m⁻¹}{(2 ｘ 3.1416)^2}`
 
m₂ = `\frac {0.322624 s² ｘ 24.5 N m⁻¹}{(6.283185)^2}`

m₂ = `\frac {7.904288 kg}{39.478}`

m₂ = 0.2002 kg

or

m₂ = 200 g ------------Ans.



************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.