A ball of density po falls from the rest from a point P onto the surface of liquid of density p in time T. It enters the liquid , stops, moves up, and returns to P in a total time 3T. Neglect viscousity, surface tension and splashing. The ratio p/po is equal to
a. 1.5
b. 2
c. 3
d. 4
Please explain briefly.
Good question!
In this question the concept used is time of ascent is equal to the time of descent.
Link: https://www.meritnation.com/ask-answer/question/time-of-ascent-and-time-of-descent-different-but-not-e/motion-in-a-straight-line/1809656
The ball takes time
T to reach from the point P to water, and after coming out reaches the point P again. This would mean that time taken to reach the point P will be same as T.
We are now left with the fact that it spent the remaining time (3T-T=)2T inside the water. Now, the force on the ball inside the water will only be buoyant force.
Now, if V is the volume of the ball, the mass will be (Volume x Density=) Vpo
Buoyant force will be Vp.
The net force inside the water will be V (po-p). Now as the ball remains for time 2T, and the force acting does not change, we know that it's motion will be symmetrical, or time T to go to a depth and then time T to come back to surface.
This motion is exactly opposite to the motion from the point P from the surface and the time taken is the same.
So, the ball must be facing a net force equal to the gravitational force, but in the opposite direction.
So, we have
Upthrust = - Weight force
V (po-p) = - V po
2 po = p
So
p/po = 2
In this question the concept used is time of ascent is equal to the time of descent.
Link: https://www.meritnation.com/ask-answer/question/time-of-ascent-and-time-of-descent-different-but-not-e/motion-in-a-straight-line/1809656
The ball takes time
T to reach from the point P to water, and after coming out reaches the point P again. This would mean that time taken to reach the point P will be same as T.
We are now left with the fact that it spent the remaining time (3T-T=)2T inside the water. Now, the force on the ball inside the water will only be buoyant force.
Now, if V is the volume of the ball, the mass will be (Volume x Density=) Vpo
Buoyant force will be Vp.
The net force inside the water will be V (po-p). Now as the ball remains for time 2T, and the force acting does not change, we know that it's motion will be symmetrical, or time T to go to a depth and then time T to come back to surface.
This motion is exactly opposite to the motion from the point P from the surface and the time taken is the same.
So, the ball must be facing a net force equal to the gravitational force, but in the opposite direction.
So, we have
Upthrust = - Weight force
V (po-p) = - V po
2 po = p
So
p/po = 2