Sir can you please check the official ans key for the 2nd question again? Correct answer is 2 not 8. You have made mistake in finding the radius of small bubbles. It won't be (r/8) but (r/2). Let me explain how : Given: radius of large bubble =r Let's imagine, Radius of small bubble = R Now volume of both the small bubbles and large bubble is equal. So, (4/3)pi (r) ^3=8*(4/3)pi(R)^3 Solving this we'll get, r=2R means R=r/2 We will use this relation later. Now S/V for large bubble =4pi(r)^2/(4/3)pi(r)^3 =3/r S/V for small bubbles =4pi(R)^2/(4/3)pi (R) ^3 =3/R =3/(r/2) (as R=r/2) =2* (3/r) So value of n=2
Sir can you please check the official ans key for the 2nd question again? Correct answer is 2 not 8.
You have made mistake in finding the radius of small bubbles. It won't be (r/8) but (r/2).
Let me explain how :
Given: radius of large bubble =r
Let's imagine, Radius of small bubble = R
Now volume of both the small bubbles and large bubble is equal.
So,
(4/3)pi (r) ^3=8*(4/3)pi(R)^3
Solving this we'll get,
r=2R means R=r/2
We will use this relation later.
Now S/V for large bubble
=4pi(r)^2/(4/3)pi(r)^3
=3/r
S/V for small bubbles
=4pi(R)^2/(4/3)pi (R) ^3
=3/R
=3/(r/2) (as R=r/2)
=2* (3/r)
So value of n=2
Thank you very much for pointing the mistake! Guess I did that in a hurry. Will pin this so others do not get confused by my wrong answer.