Please help in question I am posting

Anyone?

Length L is along slant surface and not lateral length

Hmmâ€¦ 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

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, youâ€™ll find that mgcos(alpha) = mvÂ˛/r as N = 0 at the point. Thus, vÂ˛ = 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, vÂ˛ can also be found. Now you can put the value of vÂ˛ in the equation vÂ˛ = rgcos(alpha). The vÂ˛ 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.

Bro I solved like this

But the final polynomial Coming is wierdâ€¦

Difficult to find rootsâ€¦

A cubic in cos theta I got.n

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 Limitâ€¦ Answer 3

Yes cubic in cosâ€¦

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

oh yeah 4 is right

i forgot that a/2 while applying second tangent formula

rest is correct

@Curious_Monkey

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 acceleratingâ€¦

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

Yes all this I did and got stuck on the cubic in cos. Iâ€™ll search for the solution of cubic onlineâ€¦

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

idk but thats rare in case of jee advanced

This is from mains revision package of coaching

In this question, we basically have to predict what is the initial vertical accn right? I donâ€™t see any way to predict this. Answer is given 10 m/sÂ˛ which I guessed as itâ€™s the closest but no mathematical proof?

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/sÂ˛ is the acceleration of an object under free fall and thus, the initial vertical acceleration would be 10 m/sÂ˛. Thatâ€™s the only approach I can think of.