Download App

4.1 , newtons laws of motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics4.1 , newtons laws of motion1 Mark
MCQ
A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$F=F_{0}\left(1-\left(\frac{t-T}{T}\right)^{2}\right)$

Where $F_{0}$ and $T$ are constants. The force acts only for the time internal $2 T$. The velocity $v$ of the particle after time $2 {T}$ is -

  • A
    $\frac{{F}_{0} {T}}{3 {M}}$
  • B
    $\frac{{F}_{0} {T}}{2 {M}}$
  • C
    $\frac{2{F}_{0} {T}}{{M}}$
  • ✓
    $\frac{4 {F}_{0} {T}}{3 {M}}$
✓

Answer

Correct option: D.
$\frac{4 {F}_{0} {T}}{3 {M}}$
d
${t}=0, {u}=0$

As given

${a}=\frac{{F}_{0}}{{M}}-\frac{{F}_{{o}}}{{MT}^{2}}({t}-{T})^{2}=\frac{{dv}}{{dt}}$

$\int_{0}^{v} {d} v=\int_{t=0}^{2 T}\left(\frac{F_{o}}{M}-\frac{F_{0}}{M T^{2}}(t-T)^{2}\right) d t$

$V=\left[\frac{F_{0}}{M} t\right]_{0}^{2 T}-\frac{F_{0}}{M T^{2}}\left[\frac{t^{3}}{3}-t^{2} T+T^{2} t\right]_{0}^{2 T}$

${V}=\frac{4 {F}_{0} {T}}{3 {M}}$

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 4.1 , newtons laws of motion→4.1 , newtons laws of motion — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A rope of negligible mass is wound round a hollow cylinder of mass $3\, kg$ and radius  $40\, cm$. If rope is pulled with a force of $30\, N$, then the angular acceleration  produced in the cylinder is ........ $rad\, s^{-2}$.
→
Two springs with spring constants ${K_1} = 1500\,N/m$ and ${K_2} = 3000\,N/m$ are stretched by the same force. The ratio of potential energy stored in spring will be
→
A body throws a ball upwards with velocity $v_0 = 20\, m/s$ . The wind imparts a horizontal acceleration of $4\, m/s^2$ to the ball. The angle $\theta $ from vertical at which the ball must be thrown so that the ball returns to the boy's hand is $(g = 10\, m/s^2)$
→
On any planet, the presence of atmosphere implies (${C_{rms}}$= root mean square velocity of molecules and ${V_e}$= escape velocity)
→
$A$ block of mass $m$ moves on a horizontal rough surface with initial velocity $v$. The height of the centre of mass of the block is $h$ from the surface. Consider a point $A$ on the surface.
→
In case of hydrogen and oxygen at $N.T.P.$, which of the following quantities is $/$ are the same?
→
A drop of liquid of diameter $2.8\, mm$ breaks up into $125$ identical drops. The change in energy is nearly ........ $erg$ (S.T. of liquid = $75\, dynes/cm$)
→
From the following statements, concerning ideal gas at any given temperature $T,$ select the correct one(s)
→
In a streamline flow:
→
When a tuning fork of frequency $341$ is sounded with another tuning fork, six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork, the number of beats is two per second. The natural frequency of the second tuning fork is
→