Download App

STD 12 - 2. Electric potential and capacitance — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 2. Electric potential and capacitance4 Marks
MCQ
Consider a gravity free container as shown. System is initially at rest and electric potential in the regon is $V = (y^3+2)\  J/C$. A ball of charge $q$ and mass $m$ is released from rest from base starts to move up due to electric field and collides with the shaded face as shown.If its speed just after collision is $1.5\  m/s$ and time for which ball is in contact with shaded face is $0.1\ sec$, find external force required to hold the container fixed in its position during collision assuming ball exerts constant force on wall during entire span of collision.......$N$
  • A
    $70$
  • B
    $72$
  • C
    $74$
  • ✓
    $76$
✓

Answer

Correct option: D.
$76$
d
$\mathrm{V}=\mathrm{y}^{3}+2$

$\Rightarrow \mathrm{E}=\frac{-\delta V}{\delta y} \hat{i}=-3 y^{2} \hat{j}$

$\mathrm{V}_{\mathrm{A}}=2 \mathrm{\,volt}$

$\mathrm{V}_{\mathrm{B}}=10$ volt $\left[\mathrm{V}=\mathrm{y}^{3}+2\right]$

$\mathrm{q}\left(\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{A}}\right)=\frac{1}{2} m v^{2} \Rightarrow \frac{1}{2}(8)=\frac{1}{2}(2) \,V^{2}$

$\Rightarrow \mathrm{V}=2 \mathrm{\,m} / \mathrm{s}$

So, velocity of ball before collision $ = (2{\rm{\,m}}/{\rm{s}})j$

So, velocity of ball after collision $ =  - (1.5\,{\rm{m}}/{\rm{s}})j$

change in momentum $ = m\left( {{{\overrightarrow V }_F} - {{\overrightarrow V }_i}} \right) = ( - 7\,N.S)j$

Net force $ = ( - 7)/(0.1) = ( - 70\,{\rm{N}}){\rm{j}}$

from $\mathrm{FBD}$ of ball during collision

${{\rm{F}}_{{\rm{net}} = }}{\rm{ = }}{{\rm{F}}_{{\rm{wall}}}} - {\rm{qE}}$

$\mathrm{F}_{\mathrm{wall}}=\mathrm{F}_{\mathrm{net}}+\mathrm{q} \mathrm{E}$

$=(70+6)=76 \mathrm{\,N}$

${\rm{[E}}$ at top face $ = 3{{\rm{y}}^2} = 3{(2)^2} = 12\,{\mkern 1mu} {\rm{N}}/{\rm{C]}}$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A gas is suddenly compressed to one fourth of its original volume. What will be its final pressure, if its initial pressure is $P$
→
Two infinitely long straight wires lie in the $\mathrm{xy}$-plane along the lines $\mathrm{x}=+R$. The wire located at $\mathrm{x}=+\mathrm{R}$ carries a constant current $\mathrm{I}_1$ and the wire located at $\mathrm{x}=-R$ carries a constant current $\mathrm{I}_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0, \sqrt{3} R)$ and in a plane parallel to the xy-plane. This loop carries a constant current $/$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{\mathrm{j}}$ direction. Which of the following statements regarding the magnetic field $\dot{B}$ is (are) true?

$(A)$ If $I_1=I_2$, then B' cannot be equal to zero at the origin $(0,0,0)$

$(B)$ If $\mathrm{I}_1>0$ and $\mathrm{I}_2<0$, then $\mathrm{B}$ can be equal to zero at the origin $(0,0,0)$

$(C)$ If $\mathrm{I}_1<0$ and $\mathrm{I}_2>0$, then $\mathrm{B}$ can be equal to zero at the origin $(0,0,0)$

$(D)$ If $\mathrm{I}_1=\mathrm{I}_2$, then the $\mathrm{z}$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_0 \mathrm{I}}{2 \mathrm{R}}\right)$

→
A block of mass $m$ slides down on a wedge of mass $M$ as shown in figure. Let $\vec a_1$ be the acceleration of the wedge and $\vec a_2$  the acceleration of block w.r.t. ground. $N_1$ is the normal reaction between block and wedge and $N_2$ the normal reaction between wedge and ground. Friction is absent everywhere. Select the incorrect alternative
→
Of the following pairs of species which one will have the same electronic configuration for both members?
→
The value of g on the earth's surface is $980\,cm/{\sec ^2}$. Its value at a height of $64 \,km$ from the earth's surface is ........ $cm/{\sec ^2}$

(Radius of the earth $R = 6400$ kilometers) 

→
An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by $10\, cm$. The size of the images in two situations are in the ratio $3 : 2$. What is the distance between the screen and the object?......$cm$
→
A body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi $ seconds. If the ball is removed, the length of the spring will decrease by
→
Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column $II$. In each case, a point $\mathrm{M}$ and a line $\mathrm{PQ}$ passing through $\mathrm{M}$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $\mathrm{M}$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line $PQ$. Let $B$ be the magnetic field at $\mathrm{M}$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.
Column $I$ Column $II$
$(A)$ $E=0$ $Image$ Charges are at the corners of a regular hexagon. $\mathrm{M}$ is at the centre of the hexagon. $\mathrm{PQ}$ is perpendicular to the plane of the hexagon.
$(B)$ $V \neq 0$ $Image$ Charges are on a line perpendicular to $\mathrm{PQ}$ at equal intervals. $\mathrm{M}$ is the mid-point between the two innermost charges.
$(C)$ $B=0$ $Image$ Charges are placed on two coplanar insulating rings at equal intervals. $\mathrm{M}$ is the common centre of the rings. $\mathrm{PQ}$ is perpendicular to the plane of the rings.
$(D)$ $\mu \neq 0$ $Image$ Charges are placed at the corners of a rectangle of sides $a$ and $2 a$ and at the mid points of the longer sides. $\mathrm{M}$ is at the centre of the rectangle. $\mathrm{PQ}$ is parallel to the longer sides.
  $Image$ Charges are placed on two coplanar, identical insulating rings at equal intervals. $\mathrm{M}$ is the mid-point between the centres of the rings. $\mathrm{PQ}$ is perpendicular to the line joining the centres and coplanar to the rings.

→
In an $LCR $ circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. ( $q$ is charge on the capacitor and $\tau = RC$ is Capacitive time constant). Which of the following statement is correct?
→
A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$
→