Question

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?

Answer 1

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

Answer 2

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.