When the mass attached to a spring is increas | vedclass

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

Question

(D) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$.For mass $m_1 = 4 \ kg$,the time period is $T_1 = 2\pi \sqrt{\fr

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(D) The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$.For mass $m_1 = 4 \ kg$,the time period is $T_1 = 2\pi \sqrt{\frac{4}{k}} = 2\pi \cdot \frac{2}{\sqrt{k}} = \frac{4\pi}{\sqrt{k}}$.For mass $m_2 = 9 \ kg$,the time period is $T_2 = 2\pi \sqrt{\frac{9}{k}} = 2\pi \cdot \frac{3}{\sqrt{k}} = \frac{6\pi}{\sqrt{k}}$.Given that the time period increases by $0.2\pi \ s$,we have $T_2 - T_1 = 0.2\pi$.Substituting the expressions for $T_1$ and $T_2$: $\frac{6\pi}{\sqrt{k}} - \frac{4\pi}{\sqrt{k}} = 0.2\pi$.$\frac{2\pi}{\sqrt{k}} = 0.2\pi$.Dividing both sides by $\pi$: $\frac{2}{\sqrt{k}} = 0.2$.$\sqrt{k} = \frac{2}{0.2} = 10$.Squaring both sides,we get $k = 100 \ N \ m^{-1}$.

When the mass attached to a spring is increased from $4 \ kg$ to $9 \ kg$,the time period of oscillation increases by $0.2 \pi \ s$. Then the spring constant of the spring is (in $N \ m^{-1}$)

Similar Questions

$A$ flat horizontal board moves up and down in $SHM$ with an amplitude $\alpha$. What is the shortest permissible time period of the vibration such that an object placed on the board does not lose contact with the board?

The scale of a spring balance reading from $0$ to $10 \, kg$ is $0.25 \, m$ long. $A$ body suspended from the balance oscillates vertically with a period of $\pi / 10 \, s$. The mass suspended is ..... $kg$ (neglect the mass of the spring).

How does the period of oscillation depend on the mass of the block attached to the end of a spring?

$A$ body of mass $m$ is suspended to an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

Vedclass Test Series

Exam Paper Generator

Online Exam Module