A body of mass 4.9 , kg hangs from a spring a | vedclass

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

Question

(C) Given that, mass of body $m = 4.9 \, kg$.Time period of oscillation of the spring $T = 0.5 \, s$.Acceleration due to gravity $g = 10 \, m/s^2$ and

Vedclass · Accepted Answer

$6.25 \, cm$

Vedclass · Answer

(C) Given that, mass of body $m = 4.9 \, kg$.Time period of oscillation of the spring $T = 0.5 \, s$.Acceleration due to gravity $g = 10 \, m/s^2$ and $\pi^2 = 10$.The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{m}{k}}$.Squaring both sides, we get $T^2 = 4\pi^2 \frac{m}{k}$.Rearranging for the ratio $\frac{m}{k}$, we have $\frac{m}{k} = \frac{T^2}{4\pi^2}$.Substituting the values, $\frac{m}{k} = \frac{(0.5)^2}{4 	imes 10} = \frac{0.25}{40} = 0.00625 \, kg/N$.When the mass is removed, the spring shortens by an amount $x$ equal to the extension produced by the mass in equilibrium.From Hooke's Law at equilibrium, $kx = mg$, which implies $x = \frac{m}{k} g$.Substituting the values, $x = 0.00625 	imes 10 = 0.0625 \, m$.Converting to centimeters, $x = 0.0625 	imes 100 = 6.25 \, cm$.Thus, the spring is shortened by $6.25 \, cm$.

$A$ body of mass $4.9 \, kg$ hangs from a spring and oscillates with a period $0.5 \, s$. On the removal of the body, the spring is shortened by (take $g=10 \, m/s^2, \pi^2=10$)

Similar Questions

$A$ solid cylinder of density $\rho_0$,cross-section area $A$ and length $l$ floats in a liquid of density $\rho (\rho > \rho_0)$ with its axis vertical. If it is slightly displaced downward and released,the time period of oscillation will be:

Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go,the time period of oscillation is

To make the frequency of a spring oscillator double,we have to

$A$ mass $m$ is suspended from two coupled springs connected in series. The force constants for the springs are $K_1$ and $K_2$. The time period of the suspended mass will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module