Conservation of Energy in Case of Electrostatics

Q. The closest distance of approach of an alpha particle travelling with a velocity ‘v’ towards $A{l}_{13}$ nucleus is ‘d’. The closest distance of approach of an alpha particle travelling with velocity ‘4v’ towards $F{e}_{26}$ nucleus is

1. $\frac{d}{8}$
   
2. $\frac{d}{4}$
   
3. $\frac{d}{8}$
   
4. $8d$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

An isolated, non-spherical conductor sample is shown in figure. Conductor contains a certain charge and point A is located deep inside the conductor while point B lies outside the conductor. Choose the correct statement(s) in electrostatic condition.

चित्र में एक विलगित, अगोलीय चालक नमूना दर्शाया गया है। चालक में एक निश्चित आवेश है तथा बिन्दु A चालक के अन्दर गहराई में स्थित है जबकि बिन्दु B चालक के बाहर स्थित है। स्थिरवैद्युत स्थिति में सही कथन/कथनों का चयन कीजिए।

1. Electric field at A is zero
   
   A पर विद्युत क्षेत्र शून्य है
2. Electric field at B is zero
   
   B पर विद्युत क्षेत्र शून्य है
3. Surface charge density on surface of conductor is uniform
   
   चालक के पृष्ठ पर पृष्ठीय आवेश घनत्व एकसमान है
4. Charge at location of A is zero
   
   A की स्थिति पर आवेश शून्य है

Q. Two identical particles of mass m carry a charge Q each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed $v_0$. The closed distance of approach be

1. $\frac{k{Q}^2}{mv}$
2. $\frac{4k{Q}^2}{m{v}^2}$
3. $\frac{2k{Q}^2}{m{v}^2}$
4. $\frac{k{Q}^2}{4m{v}^2}$

Q. A charged particle q is fired towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q is given speed 2v, the closest distance of approach would be: [AIEEE-2004]

1. r
2. 2r
3. r/2
4. r/4

Q. A ball of mass $1\text{g}$ and charge ${10}^{-8}\text{C}$ moves from a point $A$ having electric potential $V_A=600\text{V}$ to a point $B,$ whose electric potential is zero. Velocity of the ball at point $B$ is $20{\text{cm s}}^{-1}$. Velocity of the ball at point $A$ is
(Neglect gravitation)

1. $16.7{\text{ms}}^{-1}$
2. $16.7{\text{cm s}}^{-1}$
3. $2.8{\text{ms}}^{-1}$
4. $2.8{\text{cm s}}^{-1}$

Q.
A solid sphere and sperical shell of same mass m and same radius R are given charges +Q and -Q. Both spheres are kept on rough surface where friction is sufficient to avoid sliding. Initial seperation between spheres is 10 R. If m = 126 kg, $Q^2=23\times {10}^{-9}{C}^2$ and R = 1m.

(A)	Speed of solid sphere just before collision is	1) $\frac{3}{5}$ m/s
(B)	Speed of spherical shell just before collision is	2) 0 m/$s^2$
(C)	Speed of center of mass just before collision is	3) $\frac{5}{7}$ m/s
(D)	Acceleration of center of mass	4) Towards left
		5) Towards right

1. A $\to$ 3, B $\to$ 1, 4, C $\to$ 5, D $\to$ 5
2. A $\to$ 1, B $\to$ 3, 4, C $\to$ 4, D $\to$ 5
3. A $\to$ 1, B $\to$ 1, 4, C $\to$ 5, D $\to$ 4
4. A $\to$ 3, B $\to$ 3, 4, C $\to$ 4, D $\to$ 4

Q. A ball of mass $1\text{g}$ and charge ${10}^{-8}\text{C}$ moves from a point $A$ having electric potential $V_A=600\text{V}$ to a point $B,$ whose electric potential is zero. Velocity of the ball at point $B$ is $20{\text{cm s}}^{-1}$. Velocity of the ball at point $A$ is
(Neglect gravitation)

1. $16.7{\text{ms}}^{-1}$
2. $16.7{\text{cm s}}^{-1}$
3. $2.8{\text{ms}}^{-1}$
4. $2.8{\text{cm s}}^{-1}$