'2 balls of mass ratios 1:2 are dropped from the same height. State the ratio between their velocities when they strike the ground, the ratio of forces acting on them during motion.'

To determine the ratio of velocities when the two balls of different masses strike the ground, we need to consider the concept of gravitational potential energy being converted to kinetic energy.

We know that the potential energy (PE) of an object at a certain height is given by the product of its mass (m), the acceleration due to gravity (g), and the height (h): PE = mgh.

When the balls are released, their potential energy is converted into kinetic energy (KE) as they accelerate downward due to gravity. The equation for kinetic energy is given by KE = 0.5mv^2, where m is mass and v is velocity.

Since the balls are dropped from the same height, the potential energy they possess will be the same. Therefore, we can equate their potential energy equations:

m1gh = m2gh

Since g (acceleration due to gravity) and h (height) are constant, we can cancel them out:

m1 = 2m2 (equation 1)

This means that the mass of the first ball (m1) is twice the mass of the second ball (m2).

Now, let's consider the kinetic energy equations for each ball when they strike the ground:

KE1 = 0.5m1v1^2
KE2 = 0.5m2v2^2

Since the potential energy has been fully converted to kinetic energy, their potential energy equations are equal to their kinetic energy equations:

m1gh = KE1 (equation 2)
m2gh = KE2 (equation 3)

Since g (acceleration due to gravity) and h (height) are constant, we can equate equations (2) and (3):

KE1 = KE2

Substituting the kinetic energy equations:

0.5m1v1^2 = 0.5m2v2^2

Since we have equation 1 and m1 = 2m2:

0.5(2m2)v1^2 = 0.5m2v2^2

Canceling out common terms:

2v1^2 = v2^2

To find the ratio between their velocities, we take the square root of both sides:

sqrt(2v1^2) = sqrt(v2^2)

Simplifying:

sqrt(2)v1 = v2

Therefore, the ratio between their velocities when they strike the ground is 1:sqrt(2), or approximately 1:1.41.

Now let's move on to the ratio of forces acting on the balls during motion. The force acting on an object due to gravity is given by the equation F = mg, where m is mass and g is the acceleration due to gravity.

From equation 1, we know that m1 = 2m2. Thus, the force acting on the first ball (F1) is two times the force acting on the second ball (F2):

F1 = 2F2

Therefore, the ratio of forces acting on the balls during motion is 2:1.

Didn't Galeilo demonstrate the hit the ground at the same time, with the same velocity?

Forces? it is gravity, so the ratio is 1:2

Fb=K mass/height^2 where height is the distance frm the ball to center of Earth.