A particle of mass 1 kg and charge (1/3) Î¼C is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface. The minimum initial velocity V0 of projection of particle required if the particle just grazes the shell is

Question

A particle of mass 1 kg and charge (1/3) Î¼C is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface. The minimum initial velocity V0 of projection of particle required if the particle just grazes the shell is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-i7ghv4p2yseh.png" /> (A) √(2/3)ms- 1 (B) 2 √(2/3)ms- 1 (C) (2/3)ms- 1 (D) 1ms- 1

Tardigrade Admin · Accepted Answer

From conservation of angular momentum, mv0(r/2)=mvr ⇒ v=(v0/2) From conservation of energy, (1/2) m v02=(1/2) m v2+(1/4 π ϵ0)((q2/r)) v0=√(8/3)ms- 1

Q. A particle of mass $1 k g$ and charge $\frac{1}{3} μ C$ is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface. The minimum initial velocity $V_{0}$ of projection of particle required if the particle just grazes the shell is

$\frac{2}{3} m s^{- 1}$

$2 \frac{2}{3} m s^{- 1}$

$\frac{2}{3} m s^{- 1}$

$1 m s^{- 1}$

From conservation of angular momentum,
$m v_{0} \frac{r}{2} = m v r \Rightarrow v = \frac{v _{0}}{2}$
From conservation of energy,
$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + \frac{1}{4 π ϵ _{0}} (\frac{q ^{2}}{r})$
$v_{0} = \frac{8}{3} m s^{- 1}$

Q. A particle of mass 1kg and charge 31​μC is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface. The minimum initial velocity V0​ of projection of particle required if the particle just grazes the shell is

32​​ms−1

232​​ms−1

32​ms−1

1ms−1

From conservation of angular momentum, mv0​2r​=mvr⇒v=2v0​​ From conservation of energy, 21​mv02​=21​mv2+4πϵ0​1​(rq2​) v0​=38​​ms−1

Q. A particle of mass $1 k g$ and charge $\frac{1}{3} μ C$ is projected towards a non conducting fixed spherical shell having the same charge uniformly distributed on its surface. The minimum initial velocity $V_{0}$ of projection of particle required if the particle just grazes the shell is

$\frac{2}{3} m s^{- 1}$

$2 \frac{2}{3} m s^{- 1}$

$\frac{2}{3} m s^{- 1}$

$1 m s^{- 1}$

From conservation of angular momentum,
$m v_{0} \frac{r}{2} = m v r \Rightarrow v = \frac{v _{0}}{2}$
From conservation of energy,
$\frac{1}{2} m v_{0}^{2} = \frac{1}{2} m v^{2} + \frac{1}{4 π ϵ _{0}} (\frac{q ^{2}}{r})$
$v_{0} = \frac{8}{3} m s^{- 1}$