Consider a gravity-free container as shown. T | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The electric potential is $V = y^3 + 2$. The electric field is given by $\vec{E} = -\frac{dV}{dy} \hat{j} = -3y^2 \hat{j}$.At the base $(y=0)$, $V

Vedclass · Accepted Answer

$76$

Vedclass · Answer

(D) The electric potential is $V = y^3 + 2$. The electric field is given by $\vec{E} = -\frac{dV}{dy} \hat{j} = -3y^2 \hat{j}$.At the base $(y=0)$, $V_A = 2 	ext{ V}$. At the top face $(y=2 	ext{ m})$, $V_B = 2^3 + 2 = 10 	ext{ V}$.Using the work-energy theorem: $q(V_A - V_B) = \frac{1}{2}mv^2$. Since $q = -0.5 	ext{ C}$, we have $-0.5(2 - 10) = \frac{1}{2}(2)v^2$, which gives $4 = v^2$, so $v = 2 	ext{ m/s}$ (velocity just before collision).The velocity just before collision is $\vec{v}_i = 2 \hat{j} 	ext{ m/s}$. The velocity just after collision is $\vec{v}_f = -1.5 \hat{j} 	ext{ m/s}$.The change in momentum is $\Delta \vec{p} = m(\vec{v}_f - \vec{v}_i) = 2(-1.5 - 2)\hat{j} = -7 \hat{j} 	ext{ kg m/s}$.The average force exerted by the wall on the ball is $\vec{F}_{wall\_on\_ball} = \frac{\Delta \vec{p}}{\Delta t} = \frac{-7}{0.1} \hat{j} = -70 \hat{j} 	ext{ N}$.By Newton's third law, the force exerted by the ball on the wall is $\vec{F}_{ball\_on\_wall} = +70 \hat{j} 	ext{ N}$.Additionally, the electric field at the top face $(y=2)$ is $\vec{E} = -3(2)^2 \hat{j} = -12 \hat{j} 	ext{ N/C}$.The electric force on the ball is $\vec{F}_e = q\vec{E} = (-0.5)(-12)\hat{j} = 6 \hat{j} 	ext{ N}$.For the container to remain fixed, the external force $\vec{F}_{ext}$ must balance the force from the ball and the electric force on the ball: $\vec{F}_{ext} + \vec{F}_{ball\_on\_wall} + \vec{F}_e = 0$.$\vec{F}_{ext} + 70\hat{j} + 6\hat{j} = 0 \Rightarrow \vec{F}_{ext} = -76 \hat{j} 	ext{ N}$.The magnitude of the required external force is $76 	ext{ N}$.

Similar Questions

The figure shows a nonconducting ring which has positive and negative charge non-uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

The Van de Graaff generator is not based on

Two charged particles of mass $1 \ g$ each are placed $1 \ m$ apart. If each of these possesses $1 \ fC$ (femto coulomb) of charge,then the dominant force of interaction between them is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module