Question

Two spherical drops of radius 2cm and 1cm are falling with their terminal velocities. Find the ratio of their initial accelerations just after gravity ceases to exist:

a) 1:2
b) 2:1
c) 4:1
d) 1:4

Answer 1

To find the ratio of their initial accelerations, we need to understand the concept of terminal velocity. Terminal velocity is the constant velocity that is reached by an object when the drag force equals the gravitational force. By equating the drag forces acting on the two objects of different radii and solving for the velocities, we can find the ratio of their initial accelerations.

Step-by-step explanation:

In order to find the ratio of their initial accelerations, we need to understand the concept of terminal velocity. Terminal velocity is the constant velocity that is reached by an object when the drag force equals the gravitational force.

When two objects with different radii are falling with their terminal velocities, it means that the drag force acting on them is equal to the gravitational force acting on them.

Given that the radius of one spherical drop is 2 cm and the radius of the other drop is 1 cm, we can use the formula for the drag force, F_drag = 6πηrv, where η is the viscosity of the fluid, r is the radius of the object, and v is the velocity of the object.

Since both objects are falling with their terminal velocities, the drag forces acting on them are equal. By equating the drag forces and solving for the velocities, we can find the ratio of their initial accelerations.

Let's denote the ratio of the initial accelerations as a_1:a_2. Since the gravitational force is the same for both objects, the ratio of their velocities squared will be equal to the ratio of their radii squared: