A mass m is suspended from a spring of neglig | vedclass

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

Question

(C) The time period of a mass $m$ attached to a spring of spring constant $k$ is given by $T = 2\pi \sqrt{\frac{m}{k}}$.For the initial mass $m$,$T =

Vedclass · Accepted Answer

$\frac{9}{16}$

Vedclass · Answer

(C) The time period of a mass $m$ attached to a spring of spring constant $k$ is given by $T = 2\pi \sqrt{\frac{m}{k}}$.For the initial mass $m$,$T = 2\pi \sqrt{\frac{m}{k}}$.When the mass is increased by $m_0$,the new mass is $m' = m + m_0$. The new time period $T'$ is given as $\frac{5T}{4}$.So,$T' = 2\pi \sqrt{\frac{m + m_0}{k}} = \frac{5}{4} T$.Substituting the expression for $T$: $2\pi \sqrt{\frac{m + m_0}{k}} = \frac{5}{4} 	imes 2\pi \sqrt{\frac{m}{k}}$.Squaring both sides: $\frac{m + m_0}{k} = \frac{25}{16} \frac{m}{k}$.Canceling $k$ from both sides: $m + m_0 = \frac{25}{16} m$.Rearranging for $m_0$: $m_0 = \frac{25}{16} m - m = \frac{9}{16} m$.Therefore,the ratio $\frac{m_0}{m} = \frac{9}{16}$.

$A$ mass $m$ is suspended from a spring of negligible mass. The spring is pulled a little and then released,so that the mass executes $S.H.M.$ with a time period $T$. If the mass is increased by $m_0$,the time period becomes $\frac{5T}{4}$. The ratio $\frac{m_0}{m}$ is

Similar Questions

$A$ block of mass $m$ is at rest on another block of the same mass as shown in the figure. The lower block is attached to a spring. What is the maximum amplitude of motion such that both blocks remain in contact?

$A$ wooden block performs $SHM$ on a frictionless surface with frequency $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\vec{E}$ is switched-on as shown,then the $SHM$ of the block will be

$A$ particle of mass $m$ in a unidirectional potential field has potential energy $U(x) = \alpha + 2 \beta x^2$,where $\alpha$ and $\beta$ are positive constants. Find its time period of oscillation.

Assuming all pulleys,springs,and strings are massless. Consider all surfaces smooth. Choose the correct statement$(s)$.

Two springs,of force constants $k_1$ and $k_2$,are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values,the frequency of oscillation becomes

Vedclass Test Series

Exam Paper Generator

Online Exam Module