Question

An iron sphere of mass of 10 kg has the same diameter as an aluminum sphere of mass is 3.5 kg. Both spheres are dropped simultaneously from a tower. When they are 10 m above the ground, they have the same

• A. acceleration
• B. momenta
• C. potential energy
• D. kinetic energy

Answer 1

The correct option is A

acceleration

Given:

The mass of the iron sphere $=10kg$

The mass of the aluminum sphere $=3.5kg$

Height at which they are situated $=10m$

Finding the acceleration of the two objects:

1. As the two objects are simultaneously dropped from the same height, they fall freely under the influence of gravity.
2. So, their acceleration due to gravity remains the same for both, i.e., $9.8m{s}^{-2}$.

Finding the relation between the momenta of the two objects:

1. We know that momentum is given by the product of the mass of an object and its velocity at a given instant.
2. Mathematically, momentum is given by $p=mv$
3. As the momentum of an object is directly proportional to its mass, the momentum of the iron sphere is greater than that of the aluminum sphere.

Finding the relation between the potential energies of the two objects:

1. We know that the potential energy of an object is given by $P.E=mgh$, where $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height at which the object is situated.
2. As the potential energy is directly proportional to the mass of the object, its value for the iron sphere is greater than that of the aluminum sphere.

Finding the relation between the kinetic energies of the two objects:

1. We know that the kinetic energy of an object is given by $K.E=\frac{1}{2}m{v}^2$, where $m$ is the mass of the object, $v$ is the velocity of the object at a given instant.
2. As the kinetic energy is directly proportional to the mass of the object, its value for the iron sphere is greater than that of the aluminum sphere.

Hence, the correct option is option (A).