Question

Two particles A and B having different masses are projected from a tower with an equal speed. A is projected vertically upwards whereas B vertically downwards. When they reach the ground,
A. velocity of A is greater than that of B.
B. velocity of B is greater than the velocity of A.
C. both A and B attain the same velocity.
D. the particle with larger mass attains higher velocity.

Answer 1

Hint: When an object is thrown downwards, it loses height and also gains speed. Therefore it loses its potential energy and instead gains kinetic energy. Whereas, when an object is thrown upwards, as it gains height and it loses its speed. This will become the reason for increasing its gravitational potential energy and decreasing its kinetic energy.

Complete answer:
If we read the question carefully we will get to know that the height from which the objects are initially starts its motion is similar. Both are falling from the top of a tower. And also it has mentioned that the speed at which they are falling is also the same. The acceleration of the body will be the acceleration due to gravity itself. Therefore it will also be the same. If the particles are thrown in this way, the loss in gravitational potential of both the objects will be the same when they reach the bottom. Therefore the gain in kinetic energy of the objects will also be the same. Therefore the velocity at which it falls on the ground will also be the same.
Hence the correct answer is option C.

Note:
The gravitational potential energy of a body is found to be directly proportional to its height above the earth surface. Therefore if we double the height, the gravitational potential energy will also get doubled. Gravitational potential energy also depends on the mass of the body.