SATHEE: Work Energy and Power - Result Question 52

Work Energy and Power - Result Question 52

55. A solid cylinder of mass $3 k g$ is rolling on a horizontal surface with velocity $4 m s^{- 1}$ . It collides with a horizontal spring of force constant $200 N m^{- 1}$ . The maximum compression produced in the spring will be :

[2012]

(a) $0.5 m$

(b) $0.6 m$

(d) $0.2 m$

Show Answer

Answer:

Correct Answer: 55. (b)

Solution:

(b) At maximum compression the solid cylinder will stop so loss in K.E. of cylinder = gain in P.E. of spring

$\Rightarrow \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} = \frac{1}{2} k x^{2}$ $\Rightarrow \frac{1}{2} m v^{2} + \frac{1}{2} \frac{m R^{2}}{2} (\frac{v}{R})^{2} = \frac{1}{2} k x^{2}$ $\Rightarrow \frac{3}{4} m v^{2} = \frac{1}{2} k x^{2}$

$\Rightarrow \frac{3}{4} \times 3 \times (4)^{2} = \frac{1}{2} \times 200 x^{2}$

$\Rightarrow \frac{36}{100} = x^{2} \Rightarrow x = 0.6 m$

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Work Energy and Power - Result Question 52

55. A solid cylinder of mass 3kg is rolling on a horizontal surface with velocity 4ms−1. It collides with a horizontal spring of force constant 200Nm−1. The maximum compression produced in the spring will be :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

55. A solid cylinder of mass $3 k g$ is rolling on a horizontal surface with velocity $4 m s^{- 1}$ . It collides with a horizontal spring of force constant $200 N m^{- 1}$ . The maximum compression produced in the spring will be :