337I have tried to solve this problem but I am not sure how much correct I am. I request all the forum members to report any flaw they find in my procedure:
Initial PE= mgh
Initial KE = 0
Let velocity at that point be v.
So KE at that point= 12mv2
PE at that point = 9 x 12mv2
As Sayantan sir said, KE + PE at any point is the same.
So KE+ PE at that point = Initial PE + Initial KE.
=> 12mv2+9 x 12mv2=mgh
=> 5v2=gh
=> 4v2=2gh5
Now let the height of the stone when velocity gets doubled be H.
So, 12m(2v2)+mgH=mgh
=> 12m4v2+mgH=mgh
Replace 4v2 with 2gh5
Then H comes out to be = h2
Therefore, 4 x 12 mv2+12mgh=mgh
Therefore, the new ratio is:40.5=8:1
Thanx...
- Sayan Sinha Sorry... I gave the ratio between KE and PE. The question asks for PE:KE. So the answer, according to me, should be 1:8.
Thanx...
Sayantan Hazra The procedure of solving is fine; could have been done in a shorter way. There are two mistakes here:
Mistake 1: 5v^2 = gh; chk d nxt step
Mistake 2: You are asked to find the ratio of PE to KE at that instant; not KE to the total PE, which is what you have found out.- Sayan Sinha Yes sir. It should have been 4gh/5. I forgot to take the square of 2.
Sir, I have calculated the height of the ball at the instant when velocity gets doubled, and it comes out to be h/2 in my solution. But, I had made a mistake in calculating 4v^2. Therefore, the new H= 3h/5. Upon further calculation (similar steps as the solution I had given), the answer comes out to be 3:20...
Thanx...
Arkadyuti Banerjee Thanks guys for helping me. Looks like I had done it right only. I just needed to think straight. Thanks for your response.- Arkadyuti Banerjee Thank you Sir for helping me! How to close this thread BTW?
