Three masses 700 ,g,500 ,g,and 400 ,g are sus | vedclass

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

Question

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

Vedclass · Accepted Answer

$2 \,s$

Vedclass · Answer

(B) The time period of oscillations for a spring-mass system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $m$ is the oscillating mass and $k$ is the spring constant.Case $I$: When the $700 \,g$ mass is removed,the remaining mass is $m_1 = 500 \,g + 400 \,g = 900 \,g = 0.9 \,kg$. The time period is $T_1 = 3 \,s$.$3 = 2 \pi \sqrt{\frac{0.9}{k}} \quad \dots(i)$Case $II$: When the $500 \,g$ mass is further removed,the remaining mass is $m_2 = 400 \,g = 0.4 \,kg$. Let the new time period be $T_2$.$T_2 = 2 \pi \sqrt{\frac{0.4}{k}} \quad \dots(ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{T_2}{3} = \frac{2 \pi \sqrt{\frac{0.4}{k}}}{2 \pi \sqrt{\frac{0.9}{k}}} = \sqrt{\frac{0.4}{0.9}} = \sqrt{\frac{4}{9}} = \frac{2}{3}$$T_2 = 3 	imes \frac{2}{3} = 2 \,s$Thus,the system will oscillate with a period of $2 \,s$.

Three masses $700 \,g$,$500 \,g$,and $400 \,g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $700 \,g$ mass is removed,the system oscillates with a time period of $3 \,s$. If the $500 \,g$ mass is further removed,then it will oscillate with a period of

Similar Questions

When a mass $m$ is hung from the lower end of a spring of negligible mass,an extension $x$ is produced in the spring. The time period of oscillation is

$A$ spring having a spring constant $K$ is loaded with a mass $m$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is

Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of spring constants $K_1$ and $K_2$ respectively. The two bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitude of $B$ to that of $A$ is

The potential energy of a particle of mass $100 \,g$ moving along the $x$-axis is given by $U = 5x(x - 4)$,where $x$ is in metres. The period of oscillation is .................

Vedclass Test Series

Exam Paper Generator

Online Exam Module