Question

Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. When they hit the ground:_______.

a) the heavier one will have four times the kinetic energy of the lighter one.
b) the heavier one will have twice the kinetic energy of the lighter one.
c) the heavier one will have times the kinetic energy of the lighter one.
d) both of them will have the same kinetic energy.

Answer 1

b) the heavier one will have twice the kinetic energy of the lighter one.

Step-by-step explanation:

The kinetic energy of object with mass, m

K.E₁ = ¹/₂mv²

where;

m is mass of the object

v is the velocity of the object

Since, the two objects are falling under same acceleration due to gravity, their velocity will be increasing at the same rate

The kinetic energy of object with mass, 2m

K.E₂ = ¹/₂(2m)v²

K.E₂ = 2(¹/₂mv²)

BUT K.E₁ = ¹/₂mv²

K.E₂ = 2(K.E₁)

Therefore, the heavier one will have twice the kinetic energy of the lighter one.

b) the heavier one will have twice the kinetic energy of the lighter one.