Physics doubts

Please help in question I am posting

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Anyone?

Length L is along slant surface and not lateral length

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Hmm… what is the answer for 19th? Is it (4) ? @anon48028828

If i did take L as slant length, then there isnt any option which satisfies

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At the point the block leaves contact with the surface, normal force exerted on the block by the surface would be 0. Upon drawing the FBD, you’ll find that mgcos(alpha) = mv²/r as N = 0 at the point. Thus, v² = rgcos(alpha). Now the height descended by the block is r-rcos(alpha) from which Kinetic energy can be found and as we have the mass, v² can also be found. Now you can put the value of v² in the equation v² = rgcos(alpha). The v² found would be in terms of r, thus, r and r would get cancelled, we know the value of g and cos(alpha) can therefore be found.

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Bro I solved like this
But the final polynomial Coming is wierd…
Difficult to find roots… :pensive::persevere:

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A cubic in cos theta I got.n

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Find relation between any radius a of Strip at x

After finding a in terms of x
Use integral to find the Property R

Put Limit… Answer 3

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Yes cubic in cos…

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Yes. This is coming by taking L as lateral length right?

Brother you forget that D and d are diameter. That I will manage. Thanks for solution. @VictoryGod @Curious_Monkey

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oh yeah 4 is right
i forgot that a/2 while applying second tangent formula
rest is correct
@Curious_Monkey :love_you_gesture: :ok_hand:

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All this will be done if the hemisphere was fixed and then direct answer we know for that theta = cos-1(2/3) but here the hemisphere is also moving so we have to change frame of observation.

Will there be a pseudo force too? @Strange_Wizard since the hemisphere is actually accelerating…

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no see
momentum conservation first in x direction cuz no force in that direction
second Circular motion equation
centrepetal acceleration = mg component - N (0) = mv2/r
and third energy conservation from top to point at alpha

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Yes all this I did and got stuck on the cubic in cos. I’ll search for the solution of cubic online…


x1 should be answer but in none of the option this is coming :disappointed_relieved:

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idk but thats rare in case of jee advanced

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This is from mains revision package of coaching

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In this question, we basically have to predict what is the initial vertical accn right? I don’t see any way to predict this. Answer is given 10 m/s² which I guessed as it’s the closest but no mathematical proof?

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Anyone?

The initial vertical velocity of the falcon is given to be 0, which is a minima in the graph and thus dv/dt would be 0, which implies acceleration due to force exerted by falcon would be 0 and the falcon would intially be under free fall, and we know that g = 10 m/s² is the acceleration of an object under free fall and thus, the initial vertical acceleration would be 10 m/s². That’s the only approach I can think of.

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