A body of mass $m $ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released , it oscillates with a time period of $3\,s$ . When the mass $m$ is increased by $1\,kg$ , the time period of oscillations becomes $5\,s$ . The value of $m$ in $kg$ is
A body of mass $m $ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released , it oscillates with a time period of $3\,s$ . When the mass $m$ is increased by $1\,kg$ , the time period of oscillations becomes $5\,s$ . The value of $m$ in $kg$ is
- [NEET 2016]
- A
$\frac{16}{9}$
- B
$\frac{9}{16}$
- C
$\frac{3}{4}$
- D
$\frac{4}{3}$
Similar Questions
A block whose mass is $1 \;kg$ is fastened to a spring. The spring has a spring constant of $50\; N m ^{-1}$. The block is pulled to a distance $x=10\; cm$ from its equilibrlum position at $x=0$ on a frictionless surface from rest at $t=0 .$ Calculate the kinetic, potentlal and total energles of the block when it is $5 \;cm$ away from the mean position.
A block whose mass is $1 \;kg$ is fastened to a spring. The spring has a spring constant of $50\; N m ^{-1}$. The block is pulled to a distance $x=10\; cm$ from its equilibrlum position at $x=0$ on a frictionless surface from rest at $t=0 .$ Calculate the kinetic, potentlal and total energles of the block when it is $5 \;cm$ away from the mean position.
In figure $(A),$ mass ' $2 m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$. In figure $(B),$ mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in $(A)$ and $(B)$ are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.
In figure $(A),$ mass ' $2 m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$. In figure $(B),$ mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in $(A)$ and $(B)$ are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to $(A)$ and $(B)$ respectively follow the relation.
- [JEE MAIN 2022]
Three masses $700g, 500g$, and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3$ seconds, when the $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$
Three masses $700g, 500g$, and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3$ seconds, when the $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$
The vertical extension in a light spring by a weight of $1\, kg$ suspended from the wire is $9.8\, cm$. The period of oscillation
The vertical extension in a light spring by a weight of $1\, kg$ suspended from the wire is $9.8\, cm$. The period of oscillation
How the period of oscillation depend on the mass of block attached to the end of spring ?
How the period of oscillation depend on the mass of block attached to the end of spring ?