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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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