Assignment Gravitation Electrostatics Final

8/10/2019 Assignment Gravitation Electrostatics Final

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Physics/ AssignmentVMC 1 Gravitation - Electrostatics

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Pitam Pura, Delhi - 110034 Phone: 011-45221189 93.

Physics Assignment Gravitation - Electrostatics

Gravitation

1. If gis the acceleration due to gravity on the earths surface, the gain in the potential energy of an object of mass m

raised from the surface of the earth to a height equal to the radiusRof the earth, is :

(A)1

2mgR (B) 2mgR (C) mgR (D)

1

4mgR

2. Imagine a light planet revolving around a very massive star in a circular orbit of radius Rwith a period of revolution

T. If the gravitational force of attraction between the planet and the star is proportional to 5 2/R then :

(A) T2is proportional toR

2 (B) T

2is proportional toR

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(C) T2is proportional toR3/2 (D) T2is proportional toR3.75

3. Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces

acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while

maintaining the original mutual separation a.Find the initial velocity that should be given to each particle and also

the time period of the circular motion.

Electrostatics

4. A non-conducting ring of radius 0.5 m carries a total charge of 101 11 10. C distributed non-uniformly on its

circumference producing an electric fieldEeverywhere in space. The value of the integral 0

0

l

l

E .dl l

being

centre of the ring) volt is:

(A) +2 (B) 1 (C) 2 (D) zero

5. A charge +q is fixed at each of the pointsx= x0,x= 3x0,x= 5x0..

on thex-axis and a charge q is fixed ateach of the pointsx= 2x0,x = 4x0,x = 6x0.. . Herex0is a positive constant. Take the electric potential at a point

due to a charge Qat a distance rfrom it to be 04Q / r . Then the potential at the origin due to the above system of

charges is :

(A) zero (B)0 08 2

q

x ln (C) infinite (D)

0 0

2

4

q ln

x


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6. Three charges Q, + q and +q are placed at the vertices of a right angle

triangle (isosceles triangle) as shown. The net electrostatic energy of the

configuration is zero, if Qis equal to :

(A)1 2

q

(B)

2

2 2

q

(C) 2q (D) q

7. Two equal points charges are fixed at andx a x a on the x-axis. Another point charge Q is placed at the

origin. The change in the electrical potential energy of Q, when it is displaced by a small distancexalong the x-axis,

is approximately proportional to :

(A) x (B) x2 (C) x3 (D) 1/x

8. A metallic shell has a point charge qkept inside its cavity. Which one of the following diagrams correctly representsthe electric lines of forces?

(A) (B) (C) (D)

9. Six charges, three positive and three negative of equal magnitude

are to be placed at the vertices of a regular hexagon such that the

electric field at O is double the electric field when only onepositive charge of same magnitude is placed at R. Which of the

following arrangements of charge is possible for P, Q,R, S,Tand

Urespectively?

(A) (B)

(C) (D)

10. A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of large radius.

Both the cylinders are initially electrically neutral.

(A) a potential difference appears between the two cylinders when a charge density is given to the innercylinder.

(B) a potential difference appears between the two cylinders when a charge density is given to the outer

cylinder.

(C) no potential difference appears between the two cylinders when a uniform line charge is kept along

the axis of the cylinders.

(D) no potential difference appears between the two cylinders when same charge density is given to both

the cylinders.


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11. A spherical portion has been removed from a solid sphere having a

charge distributed uniformly in its volume as shown in the figure.

The electric field inside the emptied space is:

(A) zero everywhere (B) non-zero and uniform

(C) non-uniform (D) zero only at its centre

12. Consider a system of three charges3 3

q q and

2

3

q placed at pointsA,Band Crespectively, as shown in the figure.

Take Oto be the center of the circle of radiusR and angle CAB= 60 :

(A) The electric field at point Ois2

08

q

Rdirected along the negative x-axis

(B) The potential energy of the system is zero

(C) The magnitude of the force between the charges at CandBis2

054

q

R

(D) The potential at point Ois012

q

R

13. A disk of radius4

a having a uniformly distributed charged 6C is placed in the x-y plane with its centre at

0 02

a

. A rod of length acarrying a uniformly distributed charge 8C is placed on the x-axis from

4

ax to

5

4

ax . Two point charges 7C and 3 Care placed at 0

4 4

a a

and

3 30

4 4

a a

, respectively. Consider a

cubical surface formed by six surfaces 2 2 2

a a a

x y z . The electric flux through this cubical surface is :

(A)0

2C

(B)

0

2C

(C)

0

10C

(D)

0

12C

14. Three concentric metallic spherical shells of radiiR, 2Rand 3Rare given chargesQ1, Q2and Q3, respectively. It is

found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges

given to the shells, Q1: Q2: Q3, is :

(A) 1 : 2 : 3 (B) 1 : 3 : 5 (C) 1 : 4 :9 (D) 1 : 8 : 18

Passage for Question 15-17

The nuclear charge (Ze) is non-uniformly distributed within a

nucleus of radius R. The charge density

r (charge per unit

volume) is dependent only on the radial distance r form the centre of

the nucleus as shown in figure. The electric field is only along the

radial direction.

15. The electric field at r=R is:

(A) Independent of a (B) directly proportional to a

(C) directly proportional to a2 (D) inversely proportional to a

16. For a= 0, the value of d(maximum value of as shown in the figure) is:


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(A)3

3

4

Ze

R (B)

3

3Ze

R (C)

3

4

3

Ze

R (D)

33

Ze

R

17. The electric field within the nucleus is generally observed to be linearly dependent on r. This implies.

(A) 0a (B) 2Ra (C) a R (D) 23

Ra

One or more correct options

18. A positively charged thin metal ring of radiusRis fixed in thex-yplane with its centrer at the origin O. A negatively

charged particle Pis released from rest at the point (0, 0,z0) where 0 0z . Then the motion of Pis:

(A) periodic for all values ofz0satisfying 00 z

(B) simple harmonic for all values of z0satisfying 00 z R

(C) approximately simple harmonic provided 0z R

(D) such that Pcrosses Oand continues to move along the negativez axis towards z

19. A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere

at a distancer from its centre :

(A) increases as rincreases for r R (B) decreases as r increases for 0 r

(C) decreases asr increases for R r (D) is discontinuous at r= R

20. An elliptical cavity is carved within a perfect conductor. A positive charge qis placed at the centre of the cavity. The

points aandBare on the cavity surface as shown in the figure. Then

(A) electric field nearAin the cavity = electric field nearBin the cavity

(B) charge density atA= charge density atB

(C) potential atA= potential atB

(D) total electric field flux through a closed surface just inside cavity is 0q /

21. A few electric field lines for a system of two charges Q1and Q2

fixed at two different points on the x-axis are shown in the

figure. These lines suggest that

(A) 1 2|Q | | Q |

(B) 1 2|Q | |Q |

(C) at a finite distance to the left of Q1the electric field is zero

(D) at a finite distance to the right of Q2the electric field is zero

22. A spherical metal shellAof radiusRAand a solid metal sphereBof radius B AR R are kept far apart and each isgiven charge +Q. Now they are connected by a thin metal wire. Then

(A) 0inside

AE (B) A BQ Q (C)A B

B A

R

R

(D) on surface on surfaceBAE E

Subjective type questions

23. Two small balls having equal positive charges Q(coulomb) on each are suspended by two insulating strings of equal

length L(metre) from a hook fixed to a stand. The whole set-up is taken in a satellite into space where there is no

gravity (state of weightlessness). The angle between the strings is . And the tension in each string is .. newton.


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33. (a) A charge of Q is uniformly distributed over a spherical volume of radius R. Obtain an expression for the

energy of the system.

(b) What will be the corresponding expression for the energy needed to completely disassemble the planet earth

against the gravitational pull amongst its constituent particle?

Assume the earth to be a sphere of uniform mass density. Calculate this energy, given the product of the mass and

the radius of the earth to be 312 5 10. kg m .

(c) If the same charge of Qas in part (a) above is given to a spherical conductor of the same radiusR, what will

be the energy of the system?

34. A circular ring of radiusRwith uniform positive charge density per unit length is located in the y-z plane with its

center at the origin O. A particle of mass mand positive charge q is projected from the point 3 0 0P R on thepositivex-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that

the particle does not return to P.

35. Two isolated metallic solid spheres of radiiRand 2Rare charged such that both of these have same charge density

. The spheres are located far away from each other and connected by a thin conducting wire. Find the new charge

density on the bigger sphere.

36. A non-conducting disc of radius a uniform positive surface charge density is placed on the ground with its axis

vertical. A particle of mass mand positive charge qis dropped, along the axis of the disc from a height Hwith zero

initial velocity. The particle has 04q / m g / .

(a) Find the value ofHif the particle just reaches the disc.

(b) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.

37. Eight point charges are placed at the corners of a cube of edge

a as shown in figure. Find the work done in disassembling this

system charges.

38. Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side a. The

surface tension of the soap film is . The system of charges and planar film are in equilibrium, and

12

/ N

qa k

,

wherek is a constant. ThenNis.

39. A point charge qis placed on the top of a cone of semi vertical angle Q. show that electrical flux through the base of

cone is

0

1

2

q cos

.

40. Two point charges andq q separated by the distance 2 (fig.).

Find the flux of the electric field strength vector across a circle of

radiusR.

R

q

q


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Assignment Gravitation Electrostatics Final

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