Aman stands on a weighing machine placed on a horizontal platform… - Vidyadip

Question

Aman stands on a weighing machine placed on a horizontal platform. The machine reads $50kg$. By means of a suitable mechanism, the platform is made to execute harmonic vibrations up and down with a frequency of two vibrations per second. What will be the effect on the reading of the weighing machine? The amplitude of vibrations of platform is $5cm$. Take, $g = 10ms^{-2}$.

✓

Answer

Here. $m = 50kg. v = 2s^{-1} A = 5cm = 0.05m$ Maximum acceleration$\text{a}_\text{max}=\omega^2\text{A}$
$=(2\pi\text{v}^2)\text{A}=4\pi^2\text{v}^2\text{A}$
$=4\times\Big(\frac{22}{7}\Big)^2\times(2)^2\times0.05$
$=7.9\text{cm}^{-2}$
$\therefore$ Maximum force felt by the man $=\text{m}(\text{g}+\text{a}_\text{max})$
$=50(10+7.9)$
$=895.0\text{N}$
$=89.5\text{kgf}$
Minimum force felt by the man $=\text{m}(\text{g}-\text{a}_\text{max})$$=50(10-7.9)$
$=105.0\text{N}$
$=10.5\text{kgf}$
Hence, the reading of the weighing machine varies between 10.5kgf and 69.5kgf.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Oscillations→Oscillations — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Water drops fall freely from a tap at a height of $4.9m$. If time interval between successive drops is equal and the $4th$ drop is released when the first lands on the ground, find the separation between the second and third drops.

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity $25.0m^3$ at a temperature of $27°C$ and $1$ atm pressure.

A capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by 10% then by what percentage the rate of flow of liquid will change.

Two stars each of one solar mass ($= 2 \times 10^{30}kg$) are approaching each other for a head on collision. When they are a distance $10^9km$, their speeds are negligible. What is the speed with which they collide? The radius of each star is $10^4km.$ Assume the stars to remain undistorted until they collide. (Use the known value of G).

If the horizontal force needed for the turn in the previous problem is to be supplied by the normal force by the road, what should be the proper angle of banking?

A string of linear mass density $0.5g/cm$ and a total length $30\ cm$ is tied to a fixed wall at one end and to a frictionless ring at the other end figure, The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of $20\ cm/s.$ The pulse is symmetric about its maximum which is located at a distance of $20\ cm$ from the end joined to the ring.

Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape.
The shape of the string changes periodically with time. Find this time period.
What is the tension in the string?

The resultant of two vector $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If the direction of $\vec{Q}$ is reversed, then the resulting vector becomes $\vec{S}$. Then prove that,
$
R ^2+ S ^2=2\left( P ^2+ Q ^2\right)
$

What is the pressure inside a drop of mercury of radius 3.0 mm at room temperature? Surface tension of mercury at that temperature $\left(20^{\circ} \mathrm{C}\right)$ is $4.65 \times 10^{-1} \mathrm{Nm}^{-1}$. The atmospheric pressure is $1.01 \times 10^5 \mathrm{~Pa}$. Also give the excess pressure inside the drop.

What should be the condition for the efficiency of a Carnot engine to be equal to 1?

The initial state of a certain gas is $(P_i , V_i , T_i )$. It undergoes expansion till its volume becoms $V_f$ . Consider the following two cases:

The expansion takes place at constant temperature.
The expansion takes place at constant pressure.

Plot the $P-V$ diagram for each case. In which of the two cases, is the work done by the gas more?