Two objects a and b have the same size and shape, but a is twice as heavy as

b. when they are dropped simultaneously from a tower, they reach the ground at the same time. which has a greater momentum?

In general momentum is defined as the product of mass and velocity. It is expressed as momentum (P) = mass (m in Kgs) * velocity (v in m/s) ie P = m * v kgm/s

Given:

Two objects of same size and shape a and b

The velocity of the both the bodies are same ie velocity = v1 = v2=v - eqn 1 But they differ in heaviness as follows:

The heaviness of the object a is two times of b

ie a = 2b or a/b = 2 or a : b = 2 : 1

mass of the body m1 = 2a - - eqn-2

momentum of the body is a (P1) = 2m1 * v

mass of the body m2 = b - - eqn 3

momentum of the body b (P2) = m1 * v

the momentum of the two bodies are P1 = P2

ie m1*v1 = m2*v2

P1 : P2 = m1*v1 : m2 * v2

sub the value of v2, v1 from eqn 1, m1=2a, m2=b

P1 : P2 = 2av : bv

P1 : P2 = 2a : b

ie (P1/P2) = (2a/b) - - eqn 4

Ans : -

from the above eqn 4 - it is obvious the momentum of body a is twice of body b

ie momentum of the body a is greater.

By definition we have that momentum is the product of the mass of the object by the velocity of the object. In other words:

p = m * v

Both objects have the same speed because they reach the ground at the same time.

However, object a is heavier than object b. The weight of the objects is:

a = 2m

b = m

Therefore the momentum of a and b is

pa = 2mv

pb = mv

Object a has the greatest momentum

Answer

pa> pb

2mv> mv