To find the spring constant $(k)$ of a spring experimentally, a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in measurement of mass. The percentage error in determining value of $\mathrm{k}$ is :
JEE MAIN 2024, Diffcult
Download our app for free and get started
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
$\mathrm{T}^2 \propto \frac{\mathrm{m}}{\mathrm{k}}$
$\frac{2 \Delta \mathrm{T}}{\mathrm{T}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{\Delta \mathrm{k}}{\mathrm{k}} \%$
$\frac{\Delta \mathrm{k}}{\mathrm{k}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{2 \Delta \mathrm{T}}{\mathrm{T}} \% $
$\frac{\Delta \mathrm{k}}{\mathrm{k}} \%=(-1) \%-2(2) \%=|-5 \%|=5 \%$
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
- 1When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $y ( t )= y _{0} \sin ^{2} \omega t ,$ where $'y'$ is measured from the lower end of unstretched spring. Then $\omega$ isView Solution
- 2The time period of a simple pendulum of length $L$ as measured in an elevator descending with acceleration $\frac{g}{3}$ isView Solution
- 3The displacement of a particle executing $S.H.M.$ is given by $x=0.01 \sin 100 \pi(t+0.05)$. The time period is ........ $s$View Solution
- 4The graphs in figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graphs best represents the relationship obtained when $y$ is The total energy of the systemView Solution
- 5A body is performing simple harmonic motion with amplitude a and time period $T$. Variation of its acceleration $(f)$ with time $(t)$ is shown in figure. If at time $t$, velocity of the body is $v$, which of the following graphs is correctView Solution
- 6The $ P.E.$ of a particle executing $SHM$ at a distance $x$ from its equilibrium position isView Solution
- 7The $x$-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=4 / 3 \mathrm{~s}$ isView Solution
- 8The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$.The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is trueView Solution
- 9As per given figures, two springs of spring constants $K$ and $2\,K$ are connected to mass $m$. If the period of oscillation in figure $(a)$ is $3 s$, then the period of oscillation in figure $(b)$ will be $\sqrt{ x }$ s. The value of $x$ is$.........$View Solution
- 10Figure 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
