(A) The effective spring constant $K_{\text{eff}} = K + K$ because both springs are in parallel configuration.$K_{\text{eff}} = 2K = 2 \times 2 = 4 \,

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

(A) The effective spring constant $K_{\text{eff}} = K + K$ because both springs are in parallel configuration.$K_{\text{eff}} = 2K = 2 \times 2 = 4 \, N \, m^{-1}$.The mass of the block is $M = 490 \, g = 0.49 \, kg$.The time period $T$ of the oscillation is given by $T = 2 \pi \sqrt{\frac{M}{K_{\text{eff}}}}$.Substituting the values: $T = 2 \pi \sqrt{\frac{0.49}{4}} = 2 \pi \sqrt{\frac{49}{400}} = 2 \pi \left( \frac{7}{20} \right) = \frac{7 \pi}{10} \, s$.The number of complete oscillations $N$ in time $t = 14 \pi \, s$ is $N = \frac{t}{T}$.$N = \frac{14 \pi}{7 \pi / 10} = 14 \pi \times \frac{10}{7 \pi} = 20$.

Class 11 Physics Oscillations SHM of Spring Mass System

Medium

In the figure given below,a block of mass $M = 490 \, g$ placed on a frictionless table is connected with two springs having the same spring constant $(K = 2 \, N \, m^{-1})$. If the block is horizontally displaced through '$X$' m,then the number of complete oscillations it will make in $14 \pi$ seconds will be $.........$

JEE MAIN 2023 All JEE MAIN

A
$20$
B
$21$
C
$19$
D
$26$

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

JEE MAIN 2023 Paper All JEE MAIN years →

$A$ body of mass $m$ is attached to a spring which is oscillating with time period $6 \ s$. If the mass of the body is increased by $6 \ kg$,its time period increases by $3 \ s$. Determine the initial mass $m$. (in $kg$)

Medium

View Solution

$A$ cylindrical block of density $\rho$ is partially immersed in a liquid of density $3\rho$. The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\, cm$. The block performs $SHM$ when displaced from its mean position. [Use $g = 9.8\, m/s^2$]

View Solution

The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 \ Hz$. When the spring is replaced by two identical springs connected in series as shown in the figure,the effective frequency is:

MediumAIIMS 2016

View Solution

$A$ $3 \ kg$ block is connected as shown in the figure. The spring constants of the two springs $K_1$ and $K_2$ are $50 \ Nm^{-1}$ and $150 \ Nm^{-1}$ respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is $(g=10 \ ms^{-2})$. (in $ms^{-2}$)

MediumAP EAMCET 2024

View Solution

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. When the mass is displaced from the equilibrium position by a distance $x$ towards the right,find the restoring force.

Medium

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

$A$ body of mass $m$ is attached to a spring which is oscillating with time period $6 \ s$. If the mass of the body is increased by $6 \ kg$,its time period increases by $3 \ s$. Determine the initial mass $m$. (in $kg$)

$A$ cylindrical block of density $\rho$ is partially immersed in a liquid of density $3\rho$. The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\, cm$. The block performs $SHM$ when displaced from its mean position. [Use $g = 9.8\, m/s^2$]

The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 \ Hz$. When the spring is replaced by two identical springs connected in series as shown in the figure,the effective frequency is:

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. When the mass is displaced from the equilibrium position by a distance $x$ towards the right,find the restoring force.

Vedclass Test Series

Exam Paper Generator

Online Exam Module