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, Medium
Download our app for free and get started
$Time\, period\, of\, spring - block \,system,$
$T=2 \pi \sqrt{\frac{m}{k}}$
For given spring, $T \propto \sqrt{m}$
$\frac{T_{1}}{T_{2}} =\sqrt{\frac{m_{1}}{m_{2}}}$
$\text { Here, } T_{1} =3 \mathrm{s}, m_{1}=m, T_{2}=5 \mathrm{s}, m_{2}=m+1, m=?$
$ \frac{3}{5}=\sqrt{\frac{m}{m+1}} \text { or } \frac{9}{25}=\frac{m}{m+1}$
$25 m=9 m+9 \Rightarrow 16 m=9$
$\therefore m=\frac{9}{16} \mathrm{kg}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionAn assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. Initially the springs are relaxed. The left mass is displaced to the left while the right mass is displaced to the right and released. The resulting collision is elastic. The time period of the oscillations of the system is :-
- 2View SolutionThe total energy of a particle executing S.H.M. is proportional to
- 3View SolutionIn forced oscillations, a particle oscillates simple harmonically with a frequency equal to
- 4View SolutionFor a particle executing simple harmonic motion, which of the following statements is not correct
- 5A steady force of $120\ N$ is required to push a boat of mass $700\ kg$ through water at a constant speed of $1\ m/s$ . If the boat is fastened by a spring and held at $2\ m$ from the equilibrium position by a force of $450\ N$ , find the angular frequency of damped $SHM$ ..... $rad/s$View Solution
- 6A simple harmonic wave having an amplitude a and time period $T$ is represented by the equation $y = 5\sin \pi (t + 4)m.$ Then the value of amplitude $(a)$ in $(m)$ and time period $(T) $ in second areView Solution
- 7Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ isView Solution
- 8A simple pendulum with a metallic bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $1 / 4$ that of metal, the time period of the same pendulum will be ...........View Solution
- 9When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will beView Solution
- 10A particle is executing Simple Harmonic Motion $(SHM)$. The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will beView Solution