Custom Practice Test - 21-Aug (2024)

Custom Practice Test - 21-AugContact Number: 9667591930 / 8527521718

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Physics-Section-A

Three charges $4q,Q,$ and $q$ are in a straight line in the position of $0,l/2,$ and $l$respectively. The resultant force on $q$ will be zero if $Q$equal to:
1.$-q$
2.$-2q$
3.$\frac{-q}{2}$
4.$4q$

The electrostatic field due to a charged conductor just outside the conductor is:

1.	zero and parallel to the surface at every point inside the conductor.
2.	zero and is normal to the surface at every point inside the conductor.
3.	parallel to the surface at every point and zero inside the conductor.
4.	normal to the surface at every point and zero inside the conductor.

A long thin rod is charged such that charge per unit length of the rod is $λ$ . The rod is inserted into a hollow spherical surface of radius R. Maximum electric flux coming out the surface is
1. $\frac{λ R}{ε_{0}}$
2. $\frac{2 λ π R^{2}}{ε_{0}}$
3. $\frac{2 λ R}{ε_{0}}$
4. $\frac{2 λ R^{2}}{ε_{0}}$

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:

1. (1/√2)²
2. $(r / \sqrt[3]{2})$
3. (2r/√3)
4. (2r/3)

The spatial distribution of the electric field due to charges (A, B) is shown in figure. Which one of the following statement is correct?

1. A is -ve and B +ve; |A|=|B|
2. Both are +ve but A>B
3. Both are -ve but A>B
4. A is +ve and B -ve and |A|>|B|

Two parallel metal plates having charges +Q and -Q faces each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will
(1) become zero
(2) increase
(3) decrease
(4) remain same

7. Two equal negative charges of charge $-q$are fixed at the points $(0,a)$ and $(0,-a)$ on the $Y\text-$axis. A positive charge $Q$ is released from rest at the point $(2a,0)$ on the $X\text-$axis. The charge $Q$ will:

1.	execute simple harmonic motion about the origin.
2.	move to the origin and remain at rest.
3.	move to infinity.
4.	execute oscillatory but not simple harmonic motion.

Consider a uniform spherical charge distribution of radius $R_{1}$ centred at the origin O. In this distribution, a spherical cavity of radius $R_{2}$ ,centred atPwith distanceOP=a= $R_{1}$ − $R_{2}$ (see figure) is made. If the electric field inside the cavity at position $\vec{r}$ is $\vec{E} (\vec{r})$ ,then the correct statement(s) is(are)

(1) $\vec{E}$ is uniform, its magnitude is independent of $R_{2}$ but its direction depends on $\vec{r}$

(2) $\vec{E}$ is uniform, its magnitude independs of $R_{2}$ and its direction depends on $\vec{r}$
(3) $\vec{E}$ is uniform, its magnitude is independent of a but its direction depends on $\vec{α}$
(4) $\vec{E}$ is uniform, and both its magnitude and direction depends on $\vec{α}$

Let there be a spherically symmetric charge distribution with charge density varying as $p (r) = ρ_{0} (\frac{5}{4} - \frac{r}{R})$ upto r = R and p(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance from the origin. The electric field at a distance r. (r > R) from the origin is given by
1. $\frac{ρ_{0} r}{3 ε_{0}} (\frac{5}{4} - \frac{r}{R})$
2. $\frac{4 π ρ_{0} r}{3 ε_{0}} (\frac{5}{3} - \frac{r}{R})$
3. $\frac{ρ_{0} r}{3 ε_{0}} (\frac{5}{3} - \frac{r}{R})$
4. $\frac{4 ρ_{0} r}{3 ε_{0}} (\frac{5}{4} - \frac{r}{R})$

10.

Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when
(1) $x = \frac{d}{\sqrt{2}}$
(2) $x = \frac{d}{2}$
(3) $x = \frac{d}{2 \sqrt{2}}$
(4) $x = \frac{d}{2 \sqrt{3}}$

11.

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in
(1) (2)
(3) (4)

12.

Two small spherical balls each carrying a charge Q = 10 μC (10 micro-coulomb) are suspended by two insulating threads of equal lengths 1m each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle 60° between them, as shown in the figure. What is the tension in the threads (Given: $\frac{1}{(4 π ε_{0})} = 9 \times 10^{9} N m / C^{2}$ )

(1) 18 N
(2) 1.8 N
(3) 0.18 N
(4) None of the above

13.

A pendulum bob of mass $30 .7 \times 10^{- 6} k g$ and carrying a charge $2 \times 10^{- 8} C$ is at rest in a horizontal uniform electric field of 20000 V/m. The tension in the thread of the pendulum is $(g = 9 .8 m / s^{2})$
(1) $3 \times 10^{- 4} N$
(2) $4 \times 10^{- 4} N$
(3) $5 \times 10^{- 4} N$
(4) $6 \times 10^{- 4} N$

14.

Two charges each equal to $n q (n^{- 1} < \sqrt{3})$ are placed at the corners of an equilateral triangle of side a. The electric field at the third corner is $E_{3,} w h e r e (E_{0} = \frac{q}{4 {πε}_{0} a^{2}})$ is-
1 $E_{3} = E_{0}$
2 $E_{3} < E_{0}$
3 $E_{3} > E_{0}$
4 $E_{3} \geq E_{0}$

Physics-Section-B

15.

One metallic sphere A is given a positive charge whereas another identical metallic sphere B of the exact same mass as of A is given an equal amount of negative charge. Then:
(1) mass of A and mass of Bare the same.
(2) mass of Ais more.
(3) mass of Bis less.
(4) mass of B is more.

16.

The figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?

(1) 1
(2) 2
(3) 3
(4) 4

17. An infinite number of charges, each of charge $1$ μC, are placed on the $x$-axis with co-ordinates $x$ = 1, 2, 4, 8, ....∞. If a charge of $1$ C is kept at the origin, then what is the net force acting on $1~\text{C}$ charge?

1.	$9000$ N	2.	$12000$ N
3.	$24000$ N	4.	$36000$ N

18.

The distance between two point charges is increased by 10%. The force of interaction
1. Increases by 10%
2. Decreases by 10%
3. Decreases by 17%
4. Increases by 17%

19.

q₁, q₂, q₃ and q₄ are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law ?

1. $\oint_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) . d \vec{A} = \frac{q_{1} + q_{2} + q_{3}}{2 ε_{0}}$
2. $\oint_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) . d \vec{A} = \frac{(q_{1} + q_{2} + q_{3})}{ε_{0}}$
3. $\oint_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3}) . d \vec{A} = \frac{(q_{1} + q_{2} + q_{3} + q_{4})}{ε_{0}}$
4. $\oint_{s} ({\vec{E}}_{1} + {\vec{E}}_{2} + {\vec{E}}_{3} + {\vec{E}}_{4}) . d \vec{A} = \frac{(q_{1} + q_{2} + q_{3} + q_{4})}{ε_{0}}$

20.

A charge q is to be divided on two small conducting spheres. What should be the value of charges on the spheres so that when placed at a certain distance apart, the repulsive force between them is maximum?
1. $\frac{q}{4} a n d \frac{3 q}{4}$
2. $\frac{q}{2} a n d \frac{q}{2}$
3. $\frac{q}{3} a n d \frac{q}{3}$
4. $\frac{q}{4} a n d \frac{q}{4}$

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1.	\(9000\) N	2.	\(12000\) N
3.	\(24000\) N	4.	\(36000\) N