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Physics: Post your doubts here!

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Height initially is h/2 as center is taken. Half of it flows into the other vessel and center of remaining height is h/4. Subtract the height and you get h/4. m and g remain same.
look when will open the tap half of te water will go to y now the mass in both vessels will be 1/2 m
the centre of mass acts in he middle of the water thats why we will take haf the hieght
so it will be mgh/4 :oops: (thats what our teacher said)
thanks i got it (y)
but why do we take the centre and not the total height?
 
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anyone please explain this ! :(View attachment 44057

vertical component of velocity is zero initially for both balls as they are fired horizontally. (horizontal component of velocity remain same throughout the motion)
vertical component of velocity will increase because of gravity (9.81 ms^-2) which is same for both balls so they will both reach the ground simultaneously
so B is the correct option.
 
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Short answer, because the time taken with each speed is different.

Let's do the math behind this - suppose the distance traveled with both speeds is denoted by "s".
Suppose the time taken at 600 kmph = t(1).

Then, since Speed = Distance/Time, we can write

600 = s/t(1)
So that
t(1) = s/600

Similarly, let's do the same for the other speed. The distance traveled is still "s", the speed = 400 kmph, and the time taken to traverse this distance = t(2). So:

400 = s/t(2)
So that
t(2) = s/400

The average speed is the total distance traveled dividing by the time taken (the average velocity is different - it is equal to total displacement divided by time taken).
= (Total Distance traveled)/(Time taken to cover that distance).

Since the plane travels a distance "s" in one direction and returns the same distance "s", the total distance traveled = s+s = 2s.

The time taken = t(1) + t(2) = s/400 + s/600 = 3s/1200 + 2s/1200 = 5s/1200 = s/240

Therefore, the average speed = 2s/(s/240) = 480 kmph = C.

Hope this helped!
Good Luck for all your exams!
i got it. Thank you so much! :)
 
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Conservation of momentum : m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Over here v₁ = v₂ becuz they coalesce after impact, so we'll take both of dem = v
(m)(u) + m(0) = (m + m)(v)
mu = 2mv
u = 2v
v = u/2

K.E. = (½)mv²

Initial total K.E. = (½)mu² + (½)(m)(0)²
Initial total K.E = mu²/2

Final total K.E. = (½)(m + m)(v)²
Final total K.E. = (½)(2m)(v²)
Final total K.E. = mv²
substitute v = u/2
Final total K.E. = m(u/2)²
Final total K.E. = mu²/4
Final total K.E. = (1/2)(mu²/2)

Final K.E. is therefore half of initial K.E.
Answer: C
 
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Which formula could be correct for the speed v of the ocean waves in terms of the density p of sea water, the acceleration of free fall g, the depth of the ocean h and the wavelength, lambda?

This question needs the use of dimensional analysis - there is no theory in the syllabus that can be used to derive this, so we use dimensional analysis.

The units of speed are m/s = Meters/Second. These are the dimensions of Length and Time respectively, so we write their dimensions as LT^-1.
Density has units kg/m^3 = Kilograms/Meters^3. These are the dimensions of Mass and Length, so we write their dimension as ML^-3.
Acceleration (g) has units m/s^2 = Meters/Second^2. The dimension of this are written as LT^-2.
Depth and Wavelength both have units of Meters, so their dimensions are L.

On the left side, with speed, we have LT^-1 as the dimensions. Therefore, we must have a similar combination on the right side.

We note that density has the dimension M of mass; no other quantity given to us has this dimension, so if we introduce the density ρ on the right side, there will be no way to eliminate the dimension of mass on the right side (we want to eliminate mass, since there is no dimension M on the left-hand side in the speed of the wave).

So we can eliminate the need to use ρ.

Let's move on to the next elimination. We have acceleration g, depth and wavelength left.
The only one of these that has a dimension of time T (which we need on the left-hand side in speed) is acceleration. But this has dimensions of LT^-2. We want T^-1, as it is in speed. Therefore the only choice we have is to take the square root of acceleration g. So, we then have units on the right side of (L^0.5)*(T^-1).

We have to introduce (L^0.5) on the right side to ensure that we get LT^-1. Therefore, we can either multiply (g)^0.5 into (h)^0.5 or (λ)^0.5.
However, we can estimate that the speed depends on λ and say (gλ)^0.5, but there is little certainty in this. Are there any options provided with the question?
If so, you can carry out dimensional analysis on each one of those options, and you will obtain the right answer when the dimensions turn out to be LT^-1.

Hope this helped!
Good Luck for all your exams!
 
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persandkesh
14)This question is a tricky one indeed. First of all you need to decide at which point will you take the moment. If you look at the diagram, you'll find that you need to avoid the upper force "F" since you will not know the perpendicular distance from this force at any point on the line except at the lowest point, and at the lowest point's moment will be FH. Moreover, if we take the lowest point and calculate the moment about it, it'd be: FH = WA which is not in the given answers. The only alternative to avoid the upper F is to take the moment about the highest point on the ladder, because the moment of the upper F would be zero, and the equation will have 3 components.

By calculating moments about the highest point on the ladder. F x H + W x a = W x 2a
Thus the answer is A.

16)We know that work is the force multiplied by distance along the direction of the force. The direction of the force is obviously the field lines. So the change in work ( the change in potential energy is FS ). To make it more clear, the diagram below explains that all points on the red line have the same potential energy and all points on the orange line has the same potential energy as well because there is no change in the distance along the direction of the force. This is quiet similar to the Gravitational potential energy. If we consider the blue line to be the earth surface and we put equal masses on the pink horizontal line which has the same vertical height from Earth. This means that all the equal masses have the same potential energy.
4-jpg.12447

Ok to know whether the charge lost or gained potential energy. Think of it as a gravitational force as well... If you move an object away from Earth ( There is an attractive force towards the Earth ) then it gains energy (mgh). The field is from the left to right meaning that it is negative to the right and the charge is positive. Thus think of the right side as the surface of the Earth, the object is becomes nearer to the Earth thus it loses energy.

In short :
for potential energy, vertical height is always taken, so distance would be s.
The field is towards the right side, so left is positive and the right negative, which means that the potential energy will decrease. energy = workdone, therefore, w.d. = F x s

24)
Young Modulus is a property of the material itself not it's length or cross section. Since the two wires are both made of Steel, then they have the same Young Modulus.
 
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31)
electron would be attracted by the positive charge, so B and D are fundamentally wrong.
now since the electron is moving against the electric field, it will be deflected out of the field by the negative charge.
line of field represents the direction of the field .
so A
35)
answer is A because in tthe question it said there are 2 resistors so as one increases in resistance it requires more voltage so voltage across other one decreases
using formula V/E=R1/R1+R2 to test values you will get something similar to graph A
37)
the contact X would be adjusted around the resistor with 4 kΩ, so the max. n min. limits of p.d. across PQ wud be when its complete resistance is considered and when none is considered. at R = 4kΩ, the resistance across it is 20V
[ 4 /(4+1)] * 25 = 20V
when there is no 4kΩ resistor, p.d. across PQ becomes zero. therefore the answer is B.
 
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