Question

tance
Board & Competitive Exams (Level-1)
Two fixed solid spheres of charges Q and KQ are separated by a distance 6R. A charge - is to be projected
along the line joining their centres, so that it can reach the surface of other solid sphere of charge kQ.
ko
R
2R
0 ifk = 4, find minimum velocity to be given.
(ii) If we do not want to give any velocity, what should be the minimum value of k?​

Answer 1

Given that,

Radius of small sphere = R

Charge of small sphere= Q

Radius of big sphere = 2R

Charge of big sphere= kQ

Projected charge = -q

The force with which a charge -q is attracted towards the charge kQ from the surface of radius R having charge Q.

(i). If k = 4

We need to calculate the minimum velocity

Using formula of electrostatic force

$F = qE$

$qE=ma$

Put the value inro the formula

$q\times\dfrac{1}{4\pi\epsilon_{0}}(\dfrac{kQ}{(5R)^2}-\dfrac{-Q}{R^2})=ma$

$q\times\dfrac{1}{4\pi\epsilon_{0}}(\dfrac{kQ}{25R^2}-\dfrac{-Q}{R^2})=ma$

$a=\dfrac{Qq}{4\pi\epsilon_{0}R^2m}(\dfrac{-k}{25}+1) ......(i)$

Put the value of k

$a=\dfrac{Qq}{4\pi\epsilon_{0}R^2m}(\dfrac{-4}{25}+1)$

$a=\dfrac{Qq}{4\pi\epsilon_{0}R^2m}\times\dfrac{21}{25}$

We need to calculate the time

Using equation of motion

$s=ut+\dfrac{1}{2}at^2$

$t^2=\dfrac{2s}{a}$

Put the value into the formula

$t=\dfrac{2\times5R}{\dfrac{Qq}{4\pi\epsilon_{0}R^2m}\times\dfrac{21}{25}}$

$t=\sqrt{\dfrac{4\pi\epsilon_{0}Rm}{Qq}}\times3.45R$

We need to calculate the minimum velocity

Using equation of motion

$v = u+at$

Put the value into the formula

$v=0+\dfrac{Qq}{4\pi\epsilon_{0}R^2m}\times\dfrac{21}{25}\times\sqrt{\dfrac{4\pi\epsilon_{0}Rm}{Qq}}\times3.45R$

$v=2.8\sqrt{\dfrac{Qq}{4\pi\epsilon_{0}Rm}}$

(ii). If we do not want to give any velocity,

When there is no velocity it means acceleration will be zero.

We need to calculate the minimum value of k

Using equation (I)

$a=\dfrac{Qq}{4\pi\epsilon_{0}R^2m}(\dfrac{-k}{25}+1)$ ...(i)

Here, a = 0

Then, the value of k

$\dfrac{-k}{25}+1=0$

$k=25$

Hence, (i). The minimum velocity is $2.8\sqrt{\dfrac{Qq}{4\pi\epsilon_{0}Rm}}$.

(ii). The minimum value of k is 25.  

Answer 2

Answer:

THIS IS THE CORRECT ANSWER. HOPE IT HELPS (don't say i copied it, I was the one who kept on other websites)

Explanation: