71
Weird, Intuition says B . What should it be?
For second, Options B,D are same. And those contain the answer I think
For Third, Someone verify. I think it should be C
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16 Answers
213)
Here if you consider block and wedge as system.The only external force is the normal force to wedge.
A)correct.The final momentum of both is along horizontal direction and should be conserved.
Here momentum along vertical direction is not conserved due to action of external force N.
B)correct.from A)
C)Correct.Here there is no energy loss(no friction).The only external force is normal force and there is no displacement of wedge along this direction.Hence energy of system should remain conserved.Whether it is equal to mgh could be debatable,but i think it is relative and i think can be considered.
212)We know PE for charges on sphere=kQ/R.
Now for PE due to charge q.
Consider an uncharged solid spherical conductor.Now electric field at all pts. is zero,So the charges will realign themselves.Now the charges can align themselves in any pattern.(both on surface and inside).As long as E=0 at all points.
Now consider a gaussian surface at radius x.Here E=0,therefore Qint.=0
Again consider a gaussian surface at radius x+dx.Do the same.
Hence net charge in shell of radius x and thickness dx is =0
Therefore we can say that the conductor is made of several shells,each of which has net charge 0.
Hence PE at surface =PE at distance R/2 from centre=PE. at centre.
Now PE at centre is=PE due to shells+PE due to charge q=0+kq/3R
Hence ans=K(Q+q/3)/R
2624) consider the change in potential energy in each case. Ans C
21Rishabh I never said momentum is a scalar quantity.
Note the fact that they have asked for final momentum.
71@Swaraj, That's why I was confused. Since all the questions are ONE OPTION CORRECT One. So I had to choose only one. I agree with your answers though.
@ Aditya, I can't get what you mean by consider change in the Potential Energies. It would only be possible if they were initially it same level and then one was raised to the height by the thread. Then the energy would store into it and would yield the answer.
However, What if they are in the places as shown, they are given heats and then no loss? I think the question would make no sense then.
71@Rishabh Regarding the total energy as said by Swaraj, We can take the 0 PE level at CM of the Wedge as well, In that case it will hold.
71Hm. Okay. In that the ' h ' will pose problem.
By the way, Won't the gravity will be the external force here?
2624) consider the lower sphere. after absorbing the heat , it will expand.
thus the center of mass will rise (due to incrase in radius) thereby increasing its potential energy.
this potential energy needs to be compensated by the sphere itself and hence its temperature lowers.
accordingly in the hanging sphere , after the increase in radius , its CM will lower down thereby decreasing its PE . this change in PE causes the temperature to rise.
71Will that be so pronounced ? I mean is it too much not to ignore?
262depends upon the heat given and coeff. of expansion.
but since options given are such, you have to consider them.