Principle of Superposition

Q.

In stationary waves all particles between two nodes pass through the mean

position

1. At different times with different velocities

2. At different times with the same velocity

3. At the same time with equal velocity

4. At the same time with different velocities

Q. A charged particleof mass m having charge q remains in equillibirium at height d above a fixed charge Q. Now the charged particle is slighly displaced along the line joining the charges, show that it will execute S.H.M. and find the time period of oscillation.

Q.

Two coherent plane light waves of equal amplitude makes a small angle α(<<1) with each other. They fall almost normally on a screen. If $\lambda$ is the wavelength of light waves, the fringe width Δx of interference patterns of the two sets of wave on the screen is

Q.

The speed of transverse waves on a string depends upon

1. Linear mass density, tension

2. Mass density , length of string

3. Length of string, mass

4. Wavelength, velocity

Q.

A car has to move on a level turn of radius 45 m. If the coefficient of static friction between the tyre and the road is 2.0, find the maximum speed the car can take without skidding.

1. 20 m/s

2. 30 m/s

3. 10 m/s

4. 40 m/s

Q.

Out of the given four waves (1), (2), (3) and (4)

$y=asin(kx+\omega t)$ ...................(1)

$y=asin(\omega t-kx)$ ...................(2)

$y=acos(kx+\omega t)$ ...................(3)

$y=asin(\omega t-kx)$ ...................(4)

emitted by four different sources $S_1,S_2,S_{3}and{S}_4$ respectively, interference phenomena would be observed in space under appropriate conditions when

1. Source S₃ emits wave (3) and S₄ emits wave (4)

2. Source S₁ emits wave (1) and S₂ emits wave (2)

3. Source S₂ emits wave (2) and S₄ emits wave (4)

4. S₄ emits waves (4) and S₃ emits waves (3)

Q. Two wave pulses approaching each other are identical in shape except that one is inverted with respect to the other. At some instant the resultant displacement of particles from their mean position becomes zero. Then, at that instant velocity of the particles is

1. Zero
2. Non-zero
3. Depends on distance between the pulses
4. None of these

Q. A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_1$ on a particle placed at a distance $2R$ from the centre of the sphere. A spherical cavity of radius $\frac{R}{2}$ is now made in the sphere as shown in the figure. The sphere with the cavity now applies a gravitational force $F_2$ on the same particle. The ratio $\frac{F_1}{F_2}$ is

1. $\frac{1}{2}$
2. $\frac{3}{4}$
3. $\frac{7}{8}$
4. $\frac{9}{7}$

Q. Three charges $-q_1,+q_2$ and $-q_3$ are placed as shown in Fig. The x-component of the force on $-q_1$ is proportional to

1. $\frac{q_2}{b^2}-\frac{q_3}{a^2}\sin \theta$
2. $\frac{q_2}{b^2}-\frac{q_3}{a^2}\cos \theta$
3. $\frac{q_2}{b^2}+\frac{q_3}{a^2}\sin \theta$
4. $\frac{q_2}{b^2}+\frac{q_3}{a^2}\cos \theta$

Q. Two sinusoidal plane waves of the same frequency having intensities $I_0$ and $4I_0$ are travelling in the same direction. The resultant intensity at a point at which the waves meet with a phase difference of $\frac{\pi }{2}$ is

1. $2I_0$
2. $5I_0$
3. $9I_0$
4. $3I_0$

Q. a s†an ding wave in a pipe has five displacement nodes and five antinodes .The harmonic number of vbration is

Q. Three identical large plates are placed parallel to each other at a very small separation as shown in the figure. The central plate is given a charge $Q$. What amount of charge will flow to earth when the key is closed.(The other two plates are initially neutral)

Q.

Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitational force acting on a particle of mass m placed at the centre of the square will be

1. $\frac{24m^{2}G}{a^2}$

2. $\frac{6m^{2}G}{a^2}$

3. $\frac{4\sqrt{2}G{m}^2}{a^2}$

4. $Zero$

Q. A charged particle with charge q enters a region of constant , uniform and mutually orthogonal fields E and B with a velocity v perpendicular in both E and B , and comes out without any change in magnitude or direction of v. Then (a)v=E×B/|B|² (b)v=B×E/|B|² (c)v=E×B/|E|² (d)v=B×E/|E|² (here qantities in options which are not enclosed in square brackets are in vector form)

Q.

A person is sitting in a train which is moving with an acceleration of 10 m/$s^2$ rightwards. A pendulum is hanging from the ceiling

(P) Draw the Free Body Diagram of the bob with respect to the person sitting in the train.

(Q) Draw the same with respect to a person who's standing outside.

1. P - (I); Q - (III)

2. P - (II); Q - (IV)

3. P - (I); Q - (IV)

4. P - (II); Q - (III)

Q. Two pulses of identical shape overlap such that the displacement of the rope is momentarily zero at all points, what happens to the energy at this time.

1. Energy becomes zero
2. The total energy is in form of potential energy
3. The total energy is in form of kinetic energy
4. None of these

Q. A bullet of mass $50\text{gm}$ is fired from a gun towards a ball of mass $450\text{gm}$


The bullet hits the ball with speed $200\text{m/s}$ in horizontal direction as shown in figure, and remains inside it. Find the magnitude of velocity of system of (ball+ bullet) after collision.

1. $20\text{m/s}$
2. $10\text{m/s}$
3. $100\text{m/s}$
4. $50\text{m/s}$

Q. Two identical triangular wave pulses whose centres are initially $4\text{cm}$ apart, have been shown in figure given below. The speed of each pulse is $1\text{cm/s}$. After $2\text{second}$, the shape of resultant wave-pulse will be

1. Triangular
2. Rectangular
3. Straight line
4. None of these.

Q. Two identical triangular wave pulses whose centres are initially $4\text{cm}$ apart, have been shown in figure given below. The speed of each pulse is $1\text{cm/s}$. After $2\text{second}$, the shape of resultant wave-pulse will be

1. Triangular
2. Rectangular
3. Straight line
4. None of these.

Q. At a point P in space, the disturbance created by a travelling wave which is not sinusoidal is +10 cm, while the disturbance created by another sinusoidal wave at the the same point in space is +5 cm. What is the net displacement at the point P ?

1. 5 cm
2. 15 cm
3. \N
4. Cant comment

Q. Two waves represented by equation,
$y_1=2\sin (\pi t-0.1x)$ and $y_2=2\sin (\pi t-0.1x+\varphi )$ are superimposed. If the resultant wave has a maximum amplitude equal to $4\text{cm}$, the value of $\varphi$ is :

1. $\pi$
2. $2\pi$
3. $\frac{\pi }{2}$
4. $\frac{3\pi }{2}$

Q.

A hollow sphere of mass $m$ = 1 kg and radius $R$ = 1 m rests on a smooth horizontal surface. A simple pendulum having string of length $R$ and bob of mass $m$ = 1 kg hangs from top most point of the sphere as shown in the figure. A bullet of mass $m$ = 1 kg and velocity $v$ = 2 m/s partially penetrates the left side of the sphere. The velocity of the sphere just after collision with bullet is:

1. 1 m/s

2. 0.5 m/s

3. 1.5 m/s

4. 2 m/s

Q. What is Super Position Principle? Why it does not affect Gravitational force and electromagnetic force?

Q. Waves from two sources superpose on each other at a particular point, amplitude and frequency of both the waves are equal. The ratio of intensities when both waves reach in the same phase and when they reach with the phase difference of ${90}^{\circ }$ will be

1. $1:1$
2. $\sqrt{2}:1$
3. $2:1$
4. $4:1$

Q. $ABC$ is a right angled triangle in which $AB=3\text{cm}$ and $BC=4\text{cm}$. And $\angle ABC=\pi /2.$ The three charges $+15,+12$ and $-20\text{e.s.u}$ are placed respectively on $A,B$ and $C$. The force acting on $B$ is

1. $125$ dynes
2. $35$ dynes
3. $25$ dynes
4. Zero

Q. Standing waves have wave velocity or not??

Q. two point charges +q and each are kept at the vertices of an equilateral triangle of side l. Determine the magnitude and sign of the charge to be kept at its centroid so that the charges at the vertices remain in equilibrium.

Q. Two coherent sources, emitting waves of wavelength $\lambda$, are placed at a separation of $3\lambda$. A detector is moving around them on a large circle. The number of minima detected by it in one complete rotation is

1. $2$
2. $4$
3. $8$
4. $12$

Q. explain work energy theore

Q. Two similar spheres having +q and -q charge are kept at a certain distance. F force acts between the two. If in the middle of two spheres, another similar sphere having +q charge is kept, then it experiences a force whose magnitude and direction are

1. Zero having no direction
2. 8F towards +q charge
3. 8F towards -q charge
4. 4F towards +q charge