Home
Class 12
PHYSICS
Rain derops each of mass m falling from ...

Rain derops each of mass m falling from rest in air experience an upward force given by f= - bv where b is a constant and v is velocity of the drop. Using work energy theorem, derive an expression for
(A) `v=f(t)` i.e. velocity function of time.
(B) `(dE)/(dt)=f(t)` where E = Total machanical energy of the rain drop
( C) Draw the graphs `(dE)/(dt.(dU)/(dt) and P_("viscous")` as a function of time U is potential energy and P represent power ?

Text Solution

Verified by Experts

`(A)v=(mg)/(b)(1-e^((-bt)/(m))),(b)(dE)/(dt)=(m^(2)g^(2))/(b)(1+e^((-bt)/(m)))`
Promotional Banner

Topper's Solved these Questions

  • WORK, ENERGY AND POWER

    AAKASH INSTITUTE|Exercise EXERCISE|40 Videos

  • WORK, ENERGY AND POWER

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A)|67 Videos

  • WORK, ENERGY AND POWER

    AAKASH INSTITUTE|Exercise SECTION-I (SUBJECTIVE TYPE QUESTIONS)|6 Videos

  • WAVES

    AAKASH INSTITUTE|Exercise ASSIGNMENT ( SECTION-D ( Assertion - Reason Type Questions ))|12 Videos

Similar Questions

Explore conceptually related problems

For the function f(x)=int_(0)^(x)(sin t)/(t)dt where x>0

The motion of a body falling from rest in a resting medium is described by the equation (dv)/(dt)=a-bv , where a and b are constant. The velocity at any time t is

The motion of a body falling from rest in a resisting medium is described by the equation (dv)/(dt)=a-bv where a and b are constant . The velocity at any time t is given by

An oil drop of mass m and falls through a medium that offers a viscous drag force. F. if the velocity of the drop is constant it means that

The motion of a body falling from rest in a medium is given by equation, (dv)/(dt)=1-2v . The velocity at any time t is

Two rain drops of same radius r falling with terminal velocity v merge and from a bigger drop of radius R. The terminal velocity of the bigger drop is

An equation relating to the stability of an aeroplane is given by (dv)/(dt) = g cos alpha - kv , where v is the velocity and g, alpha, k are constants. Find an expression for the velocity if v = 0 at t =0

An oil drop of mass m fall through air with a terminal velocity in the presence of upward electric field of intensity E . the drop carries a charge +q . R is the viscous drag force and f is the buoyancy force . Them for the motion of the drop.

Starting from rest, the acceleration of a particle is a=2(t-1) . The velocity (i.e. v=int" a dt " ) of the particle at t=10 s is :-