Download App

3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
The displacement $x$ of a particle depend on time $t$ as $x = \alpha {t^{^2}} - \beta {t^3}$ 
  • A
    particle will return to its starting point after time $\frac{\alpha }{\beta }$
  • B
    the particle will come to rest after time $\frac{2\alpha }{3\beta }$
  • C
    the initial velocity of the particle was zero but its initial acceleration was not zero. 
  • ✓
    All of the above
✓

Answer

Correct option: D.
All of the above
d
Given, $x=\alpha t^2-\beta t^3$
Particle will return to its starting point when, $x =\alpha t ^2-\beta t ^3=0$
or,
$t=\frac{\alpha}{\beta}$
Velocity $= v =\frac{ dx }{ dt }=2 t \alpha-3 \beta t ^2 \ldots \ldots (1)$
at $t =0, v =0$ so the initial velocity zero.
Acceleration $= a =\frac{ dv }{ dt }=2 \alpha-6 t \beta \ldots \ldots(2)$
at $t =0, a =2 \alpha$ so initial acceleration does not zero.
The particle will come to rest when, 2 t $\alpha-3 \beta t ^2=0$ from $(1)$
or, $t=\frac{2 \alpha}{3 \beta}$
$At , t =\frac{\alpha}{3 \beta}, a =2 \alpha-6 \beta\left(\frac{\alpha}{3 \beta}\right)=0$
so net force $= ma =0$, thus no net force act on the particle when $t =\frac{\alpha}{3 \beta}$

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 3.2 , motion in plane→3.2 , motion in plane — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

When the speed of a moving body is doubled
→
Each of the two strings of length $51.6\,\, cm$ and $49.1\,\,  cm$ are tensioned separately by $20\,\, N$ force. Mass per unit length of both the strings is same and equal to $1\,\, g/m.$ When both the strings vibrate simultaneously the number of beats is
→
A stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string ? (Length of stick is same in all scenarios)
→
A uniform rope having some mass hanges vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed $(v)$ of the wave pulse varies with height $(h)$ from the lower end as:
→
When the body is suspended from the center of gravity in a pendulum the time period of the mass pendulum will be :
→
Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{ P }$ of magnitude $100 \;N$ is applied at point $A$ of the frame. Suppose the force is $\overrightarrow{ P }$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ............

[Given : $\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819$ $\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]$

 

→
Identify the pair of physical quantities which have different dimensions 
→
If a liquid neither falls nor rise in a capillary tube, then the angle of contact between the liquid and the capillary material will be:
→
A particle is moving along a straight line with increasing speed. Its angular momentum about a fixed point on this line ............
→
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
→