Download App

5.work,energy,power and collision — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics5.work,energy,power and collision1 Mark
MCQ
If $F=2 x^2-3 x-2$, then select the correct statement
  • A
    $x=2$ is the position of stable equilibrium
  • B
    $x=-\frac{1}{2}$ is the position of unstable equilibrium
  • ✓
    $x=-\frac{1}{2}$ is the position of stable equilibrium
  • D
    $x=2$ is the position of neutral equilibrium
✓

Answer

Correct option: C.
$x=-\frac{1}{2}$ is the position of stable equilibrium
c
(c)

$F=2 x^2-3 x-2$

Putting $F=0$

$2 x^2-3 x-2=0$

$2 x^2-4 x+x-2=0$

$2 x(x-2)+(x-2)=0$

$(x-2)(2 x+1)=0$

$\Rightarrow x=2, \quad x=\frac{-1}{2}$

$\frac{d^2 v}{d x^2}=\frac{-d F}{d x}=-(4 x-3)$

at $x=\frac{-1}{2}$

$\frac{d^2 v}{d x^2} > 0 \quad \Rightarrow$ Stable equilibrium

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 "M.C.Q (1 Marks)" from 5.work,energy,power and collision→5.work,energy,power and collision — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A steel wire of length $3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)$ and a copper wire of length $4.4\,M$ $\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)$, both of radius $1.4\,mm$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\,mm$. The load applied, in Newton, will be. (Given $\pi=\frac{22}{7}$)
→
A hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$, hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first sets in ......... $K$
→
A ball of mass $0.15\, \mathrm{~kg}$ is dropped from a height $10\, \mathrm{~m}$, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $\left(\mathrm{g}=10 \,\mathrm{~m} / \mathrm{s}^{2}\right)$ nearly : (In $\mathrm{kg}\, \mathrm{m} / \mathrm{s}$)
→
If the speed of the wave shown in the figure is $330m/s$ in the given medium, then the equation of the wave propagating in the positive $x-$direction will be (all quantities are in $M.K.S.$ units)
→
A constant force acting on a body of mass of $5\,kg$ changes its speed from $5\,ms^{-1}$ to $10\,ms^{-1}$ in $10\,s$ without changing the direction of motion. The force acting on the body is  ......... $N$
→
If $10^{22}$ gas molecules each of mass $10^{-26}\, kg$ collide with a surface (perpendicular to it)elastically per second over an area $1\, m^2$ with a speed $10^4\,m/s$, the pressure exerted by the gas molecules will be of the order of
→
A rifle bullet loses $1/20th$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is
→
A man spinning in free space changes the shape of his body e.g. by stretching his arms or curling up then, which of the following physical quantity will remain constant:
→
Two different types of rubber are found to have the stress-strain curves as shown. Then
→
The energy (in $eV$) possessed by a neon atom at $27^{\circ} C$ is ..............
→