When a body of mass $1.0\, kg$ is suspended from a certain light spring hanging vertically, its length increases by $5\, cm$. By suspending $2.0\, kg$ block to the spring and if the block is pulled through $10\, cm$ and released the maximum velocity in it in $m/s$ is : (Acceleration due to gravity $ = 10\,m/{s^2})$
A$0.5$
B$1$
C$2$
D$4$
Medium
Download our app for free and get started
B$1$
b (b) Initially when $1\, kg$ mass is suspended then by using $F = kx$
$ \Rightarrow mg = kx$
$ \Rightarrow k = \frac{{mg}}{x} = \frac{{1 \times 10}}{{5 \times {{10}^{ - 2}}}} = 200\frac{N}{m}$
Further, the angular frequency of oscillation of $2\, kg$ mass is $\omega = \sqrt {\frac{k}{M}} = \sqrt {\frac{{200}}{2}} = 10\,rad/sec$
Hence, ${v_{\max }} = a\omega = (10 \times {10^{ - 2}}) \times 10 = 1\,m/s$
Download our app
and 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.*
Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes
A person of mass $M$ is, sitting on a swing of length $L$ and swinging with an angular amplitude $\theta_0$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $l\, ( l < < L)$, is close to
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10\,s^{-1}$. At, $t = 0$ the displacement is $5\, m$. What is the maximum acceleration ? The initial phase is $\frac{\pi }{4}$
When an oscillator completes $100$ oscillations its amplitude reduced to $\frac{1}{3}$ of initial value. What will be its amplitude, when it completes $200$ oscillations?
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 :
A cylindrical block of wood (density $= 650\, kg\, m^{-3}$), of base area $30\,cm^2$ and height $54\, cm$, floats in a liquid of density $900\, kg\, m^{-3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... $cm$ (nearly)
This is the position time graph of a mass on spring. What can you say about the velocity and force at the instant indicated by dashed line ? (positive direction is to the right)
A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will be