Home
Class 12
MATHS
If r is the radius, S the surface area a...

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that
(ii) `(dV)/(dS) oo r`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|6 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|9 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos

Similar Questions

Explore conceptually related problems

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (i) (dV)/(dt)=4pir^(2)(dr)/(dt)

If r and T are radius and surface tension of a spherical soap bubble respectively then find the charge needed to double the radius of bubble.

Knowledge Check

  • If S be the surface area of V be the volume of a sphere of radius r. Then (dv)/(dt) = (r)/(k) (ds)/(dt) . Value of k is

    A
    `(1)/(2)`
    B
    `(1)/(4)`
    C
    2
    D
    4

  • Which of the following is the ratio of the surface area of the sphere with radius r to its volume?

    A
    `4/pi`
    B
    `3/r`
    C
    `r/4`
    D
    `r/pi`

    • Similar Questions

    Explore conceptually related problems

    If the radius and surface tension of a spherical soap bubble be r and T respectively. Find the charge uniformly distributed over the outer surface of the bubble, is required to double its radius. (Given that atmospheric pressure is P_(0) and inside temperature of the bubble during expansion remains constant.)

    The work done in increasing the radius of a soap bubble from R to 3 R is

    If the radius and surface tension of a spherical soap bubble are 'R' and 'T' respectively, Then show that the charge required to double its radius would be 8piR ,[epsilon_(0)R[7p_(0)R+12T]]^(1/2) . Where p_(0) is the atmospheric pressure.

    On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If rlt ltR and the surface tension of water is T, value of r just before bubbles detach is: (density of water is rho_w )

    On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If rlt ltR and the surface tension of water is T, value of r just before bubbles detach is: (density of water is rho_w )

    Twenty seven solid iron spheres, each of radius r and surface area S are melted toform a sphere with surface area \ Sprimedot Find the(i) radius rprime of the new sphere, (ii) ratio of S a n d Sprimedot

    Home
    Profile