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Option : (c) 0 and 0

Option : (a) spheres

Option : (a) \(\frac{1}{4\pi∈_0}\) \(\frac{2q}{L}\) \((1-\frac{1}{\sqrt 5})\)

(1). (b) f,h,j

(2). (c) \(\frac{1}{2}\)A

(3). (d) 4.5 W

(4). (c) 2.5 V

Given r = 3.0 t i + 2.0 t² j + 5.0  

differentiating both sides with respect to time t,

dr/dt = d/dt(3.0 t i + 2.0 t² j + 5.0 )

v = 3.0 i + 2x2 t^2-1 j + 0

v = 3.0 i + 4 t j 

Hence option (b) is the correct answer.

Correct option is (a)  \(\frac12\)mω²a²

y₁ = a sin ωt

y₂ = 2a sin(ωt + 2π/3)

then

Resultant amplitude = \(\sqrt{a^2+(2a)^2+2\times2a\times a cos 120^\circ}\)

 = \(\sqrt{a^2+4a^2-4a^2} \) 

 = a

Maximum kinetic energy E = \(\frac12\)mω²a²

y = A sin(kx-ωt) travels in direction of positive x axis & has vibrations along x axis.

y = A sin(kx+ωt) travels in direction of negative x axis & has vibrations along y axis.

Both equations represent transverse waves.

A particular waveform travels right along the x axis from left.

Difference between damped and forced oscillation. An object or a system is oscillating in its own natural frequency without the interference of an external periodical force or initial motion. Damped oscillation is similar to forced oscillation except that it has continuous and repeated force as it is going.

Three oxygen compounds of iron are known: ferrous oxide, FeO; ferric oxide, Fe₂O₃; and ferrosoferric oxide, or ferroferric oxide, Fe₃O₄, which contains iron in both +2 and +3 oxidation states. Ferrous oxide is a greenish to black powder used primarily as a pigment for glasses.

2 is the smallest prime number.

assuming that all the bees do an equal amount of work in an equal time span.

(a) 40 bees finish 1 work in 30 hours.

=> (b) 40 bees will finish 1/30 work in 1 hour.

=> (c) 1 bee will finish 1/1200 work in 1 hour.

=> (d) 1 bee will finish 1 work alone in 1200 hours.

considering statement (b): 

40 bees will finish (10/30=)1/3 work in 10 hours. 

remaining work to be done= 1-1/3 = 2/3 work, and

remaining number of bees= 40-15 = 25 bees

Now, 25 bees have to do the remaining (2/3)^rd work.

considering statement (d): 

25 bees will finish 1 work in = 1200/25 hours.

So, 25 bees will finish remaining (2/3)^rd work in = (1200/25) * (2/3) = 32 hours 

Let x=0⋅125125125
∴1000x=125.125125125...
Subtract 999x=125⋅0000000=125
∴x= 125/999

Two differences between interference and diffraction are as follows—

Interference

1. It is due to the super position.

2. In interferance patter, the dark fringes are usually almost perfectly dark.

Diffraction

1. It is due to the super position of secondary wavelets originating from the different points of the same wave front.

2. In diffraction pattern, the dark fringes are not perfectly dark.

Current = 2A
 time = 10 minutes = 10 x 60 = 600 seconds
 charge (Q) = current (I) xTime (T) 
   Q = 2 x 600 = 1200 c

Given:

Distance she goes by car = 150 km

Distance she comes back by car = 150 km

Time taken by her in going = 10 hours

Time taken by her in coming back = 5 hours

Formula Used: 

Average Speed = Total distance/Total time

Calculation: 

Total distance covered by her = Distance she goes by car + Distance she comes back by car

Total Distance = 150 + 150 = 300 km

Total time = Time taken by her in going + Time taken by her in coming back

Total time = 10 + 5 = 15 hours

Average Speed of car = 300/15 = 20 Km/h

∴ The Average Speed of the car is 20 km/h.

Given:

Total distance = 60 + 180 = 240 km.

 First 60 km is covered by speed 60 km/hr.

Average speed = 120 km/hr

Formula used:

Time = distance / speed

Calculation:

Hence time for first 60 km = distance / speed

⇒ 60 km / (60 km/hr) = 1 hour

Time taken for total travel of 240 km with average speed 120 km/hr = 240/120 = 2 hour.

Total time = 2 hour

60 km is travelled in  first 1 hour.

Now,

Required speed for remaining 180 km in remaining time 1 hour = 180 / 1

⇒ 180 km/hr

a. At the time of sunset, Light rays have to travel very long distances through air. Hence Light rays are scattered. Light rays like blue with shorter wavelength get lost due to scattering but rays with longer wavelength remain because it gets less scattering.

b. In moon there is no atmosphere and therefore scattering of light does not take place.

a. Dispersion

b. Scattering

c. Red

d. Refraction

1. Violet.

2. Red

3. The deviation of colour is minimum for the colour with more wavelength when the composite light passes through the prism. When the wavelength of the colour decreases, the deviation increases.

1. Violet

2. Red.

3. Differences in wavelength

In the morning and in the evening.

a. There is no scattering for the light around the moon since there is no atmosphere around it. Hence the sky of moon appears dark. 

b. Raindrops come down faster during rain. The distance travelled by a drop in 1/16 of a second appears like a glass rod due to persistence of vision. 

c. When viewed from a height the observer can see points at 42.70 upwards, downwards as well as sideways. Hence rainbow is seen as a circle.

d. In cities there will be large particles in the atmosphere. Hence all colours of light scatter equally.

About internal reflection - One time

In the opposite direction (west)

Red colour seen at the upper edge of the rainbow.

The sunlight undergoes two times refraction in the water drop.

The colour seen at the inner edge of a rainbow is Violet.

Violet colour seen at the lower edge.

The white light separates into its component colours when it passes through the first prism.

The colours formed by the first prism recombine to form white light when it passes through the second prism.

1. Irregular

2. Yes, scattering is the partial and irregular reflection of light. The colours in sunlight undergo scattering when they fall on the particles in the atmosphere. Sunlight reaches in the rooms and under the trees by this method.

1. Very near to the white colour.

2. Light from the seven colours of the colour disc falls continuously on the retina and due to the persistence of vision, disc appears as white.

3. 

• A torch rotated rapidly appears as an illuminated circle.
• Sparkler’s trail effect.
• Colour – top
• Thaumatrope
• Kaleidoscopic colour-top.
• Rubber pencil trick.
• LED POV displays
• Revolving wheels,
• Rotation of fan leafs

During sunset, the sunlight travels I maximum distance through the atmosphere to reach in our eyes. So red also I undergo scattering. So the horizon appears red.

a. Cyan 

b. Due to persistence of vision 

c. In green colour On rotating the disc faster, the disc appears white due to persistence of vision. The cyan appears as green since it reflects green light.

a. Magenta 

b. Visible light, ultra violet radiations

c. (i) Higher wavelength than that of visible light; becomes the reason for the heat. of the sunlight. 

(ii) Used to take photograph of distant objects, remote sensing, secret signaling, for controlling robots.

Myopia -

b. Images formed in front of the retina

d. Power of the eye lens increases

e. Suitable power of concave lens is used to solve this problem 

Hypermetropia -

a. Image is formed behind the retina

c. Power of the eye lens decreases

f. Suitable power of convex lens is used to solve this problem

Violet, Blue, Green, Red

Correct Answer is: (d) 0.2 mm

LC = 1 MSD - 1 VSD = 1 mm - 16/20 mm = 0.2 mm.

f = 10 m for v = 50/7 m, u = -25 m

for v = 25/3, u =-50 m, t = 30 s

speed = (25 m/30 s) = 3 Km /hr

Correct option is D) sky

Slope of line = - 1/2,

∴ λ = 12 yr^-1, t_1/2 = 0.693/λ =1.386 yr

4.16 yr = 3t_1/2, ∴ p =2³ = 8.

Yellow lights are strictly used for fog situations, and for construction, so you can tell what is what on the road. Yellow has high wavelength, so yellow light is scattered the least by air molecules.

Nuclear energy   is not an example of a biomass energy source. 

Yellow. Others are primary colours

BaCl₂(aq) + Na₂SO₄(aq) → 2NaCl(aq) + BaSO₄ ↓(s) white

Correct answer is: a. Ultraviolet

Dispersion – Refraction

a. Yellow – it is a secondary colour The rest are primary colours

b. Sound- it is a mechanical wave The rest are electromagnetic waves

white: Reflects all colours of light.