Question

Two objects of the same mass fall from the same height of two smooth fixed inclined planes different angles. When they reach the bottom, they should have the same :

• A. Kinetic energy
• B. impulse of the normal reaction by the inclined planes
• C. Momentum
• D. The horizontal components of their momentum

Answer 1

Answer: (A)

Kinetic energy

Answer 2

By the principle of conservation of mechanical energy, since the planes are smooth (no friction) and the objects start from the same height with the same mass, their initial potential energy is converted entirely into kinetic energy at the bottom. Thus, $mgh = \frac{1}{2}mv^2$. As 'm' and 'h' are the same for both objects, their final kinetic energy ($mgh$) will be the same. Other quantities like impulse of normal reaction, momentum (vector), and horizontal component of momentum depend on the angle of inclination, which is different for the two planes.