A tray of mass 12 ,kg is supported by two ide | vedclass

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

Question

(C) Mass of the tray, $m = 12 \,kg$. Time period, $T = 1.5 \,s$. Let $k$ be the spring constant of each spring. Since the springs are connected in par

Vedclass · Accepted Answer

$105 \,Nm^{-1}$

Vedclass · Answer

(C) Mass of the tray, $m = 12 \,kg$. Time period, $T = 1.5 \,s$. Let $k$ be the spring constant of each spring. Since the springs are connected in parallel, the effective spring constant is $k_{	ext{net}} = k + k = 2k$. The time period of a mass-spring system is given by $T = 2\pi \sqrt{\frac{m}{k_{	ext{net}}}}$. Substituting the values, we get $1.5 = 2\pi \sqrt{\frac{12}{2k}}$. $1.5 = 2\pi \sqrt{\frac{6}{k}}$. Squaring both sides, we have $(1.5)^2 = (2\pi)^2 \cdot \frac{6}{k}$. $2.25 = 4\pi^2 \cdot \frac{6}{k}$. $k = \frac{24\pi^2}{2.25} \approx \frac{24 	imes 9.87}{2.25} \approx 105.28 \,Nm^{-1}$. Thus, the spring constant of each spring is approximately $105 \,Nm^{-1}$.

$A$ tray of mass $12 \,kg$ is supported by two identical springs as shown in the figure. When the tray is pressed down slightly and then released, it executes $SHM$ with a time period of $1.5 \,s$. The spring constant of each spring is

Similar Questions

In the arrangement given in the figure,if the block of mass $m$ is displaced,the frequency is given by:

For the system given below,find the angular frequency of oscillation.

$A$ particle of mass $m$ is attached to three identical springs $A, B$ and $C$ each of force constant $k$ as shown in the figure. If the particle of mass $m$ is pushed slightly against the spring $A$ and released,then the time period of oscillations is

The equivalent spring constant of the system as shown in the figure will be:

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 $g = 10 \ m/s^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module