(B) The time period of a spring-block system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.For a given spring,$T \propto \sqrt{m}$.Therefore,$\frac{T_{1}

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The time period of a spring-block system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.For a given spring,$T \propto \sqrt{m}$.Therefore,$\frac{T_{1}}{T_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$.Here,$T_{1} = 3 \ s$,$m_{1} = m$,$T_{2} = 5 \ s$,and $m_{2} = m + 1$.Substituting the values: $\frac{3}{5} = \sqrt{\frac{m}{m+1}}$.Squaring both sides: $\frac{9}{25} = \frac{m}{m+1}$.Cross-multiplying: $9(m + 1) = 25m \Rightarrow 9m + 9 = 25m$.$16m = 9 \Rightarrow m = \frac{9}{16} \ kg$.

Class 11 Physics Oscillations SHM of Spring Mass System

Medium

$A$ body of mass $m$ is attached to the lower end of a spring whose upper end is fixed. The mass of the spring is negligible. When the mass $m$ is pulled down slightly and released,it oscillates with a time period of $3 \ s$. When the mass $m$ is increased by $1 \ kg$,the time period of oscillation becomes $5 \ s$. What is the value of $m$ in $kg$?

NEET 2016 All NEET

A
$\frac{16}{9}$
B
$\frac{9}{16}$
C
$\frac{3}{4}$
D
$\frac{4}{3}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Oscillations

Subtopic

SHM of Spring Mass System

Previous Year

NEET 2016 Paper All NEET years →

Find the maximum amplitude (in $cm$) of the $SHM$ such that block $A$ will not slip on block $B$. Given: spring constant $K = 100 \ N/m$,mass of block $A$ $m_A = 0.25 \ kg$,mass of block $B$ $m_B = 1.25 \ kg$,and coefficient of friction between $A$ and $B$ is $\mu = 0.4$. Take $g = 10 \ m/s^2$.

DifficultAIIMS 2019

View Solution

In the provided figure,two bodies $A$ and $B$ of masses $200 \, g$ and $800 \, g$ are attached to a system of springs. The springs are kept in a stretched position when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $..... \, rad/s$ when $k = 20 \, N/m$.

DifficultJEE MAIN 2021

View Solution

$A$ mass $m_1$ performs $S.H.M.$ with amplitude $A$ while connected to a horizontal spring. While mass $m_1$ is passing through the mean position, another mass $m_2$ $(m_2 < m_1)$ is placed on it so that both masses move together with amplitude $A_1$. The ratio of $A/A_1$ is

DifficultMHT CET 2026

View Solution

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $K_A$ and $K_B$ respectively. The maximum velocities of the particles during oscillations are equal. The ratio of the amplitude of '$B$' to that of '$A$' is

DifficultMHT CET 2026

View Solution

$A$ mass attached to a spring performs $S.H.M.$ whose displacement is $x = 3 \times 10^{-3} \cos(2\pi t) \text{ m}$. The time taken to obtain maximum speed for the first time is (in $s$):

DifficultMHT CET 2026

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

Find the maximum amplitude (in $cm$) of the $SHM$ such that block $A$ will not slip on block $B$. Given: spring constant $K = 100 \ N/m$,mass of block $A$ $m_A = 0.25 \ kg$,mass of block $B$ $m_B = 1.25 \ kg$,and coefficient of friction between $A$ and $B$ is $\mu = 0.4$. Take $g = 10 \ m/s^2$.

$A$ mass $m_1$ performs $S.H.M.$ with amplitude $A$ while connected to a horizontal spring. While mass $m_1$ is passing through the mean position, another mass $m_2$ $(m_2 < m_1)$ is placed on it so that both masses move together with amplitude $A_1$. The ratio of $A/A_1$ is

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $K_A$ and $K_B$ respectively. The maximum velocities of the particles during oscillations are equal. The ratio of the amplitude of '$B$' to that of '$A$' is

$A$ mass attached to a spring performs $S.H.M.$ whose displacement is $x = 3 \times 10^{-3} \cos(2\pi t) \text{ m}$. The time taken to obtain maximum speed for the first time is (in $s$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module