Three blocks of masses 700 ,g,500 ,g,and 400 | vedclass

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

Question

(B) The period of oscillation for a spring-mass system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $m$ is the total mass and $k$ is the spring co

Vedclass · Accepted Answer

$2 \,s$

Vedclass · Answer

(B) The period of oscillation for a spring-mass system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $m$ is the total mass and $k$ is the spring constant.Case $1$: When the $700 \,g$ block is removed,the remaining mass is $m_1 = (500 + 400) \,g = 900 \,g = 0.9 \,kg$.The period is $T_1 = 3 \,s$.So,$3 = 2 \pi \sqrt{\frac{0.9}{k}}$.Squaring both sides: $9 = 4 \pi^2 \left( \frac{0.9}{k} ight) \Rightarrow k = \frac{4 \pi^2 	imes 0.9}{9} = 0.4 \pi^2 \,N/m$.Case $2$: When both $700 \,g$ and $500 \,g$ blocks are removed,the remaining mass is $m_2 = 400 \,g = 0.4 \,kg$.The new period $T_2$ is given by:$T_2 = 2 \pi \sqrt{\frac{m_2}{k}} = 2 \pi \sqrt{\frac{0.4}{0.4 \pi^2}}$.$T_2 = 2 \pi \sqrt{\frac{1}{\pi^2}} = 2 \pi \left( \frac{1}{\pi} ight) = 2 \,s$.

Similar Questions

The vertical extension in a light spring by a weight of $1\, kg$ suspended from it is $9.8\, cm$. What is the period of oscillation?

$A$ block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in the figure. The block is displaced by $x$ towards the right and released. The velocity of the block when it is at $x/2$ will be

$A$ spring of length $l$ and force constant $k$ is attached to a mass $m$ and oscillates with frequency $f_1$. If the spring is cut into two equal parts and one part is attached to the same mass $m$ to oscillate,its frequency becomes $f_2$. Find the relation between $f_1$ and $f_2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module