Question

In the previous question, the smallest kinetic energy at the bottom of the incline will be achieved by
(a) the solid sphere
(b) the hollow sphere
(c) the disc
(d) all will achieve same kinetic energy.

Answer 1

The smallest kinetic energy at the bottom of the incline will be achieved by all will achieve same kinetic energy.

Explanation:

Step 1:

According to the problem, there is no friction on the slope, as a result, the only force on each of these artifacts along the slope is their portion of the weight (or force of gravity) that the relationship would give;

                       F = mg.sinθ.

                Acceleration = Forces/mass

                      a = (mg.sinθ)/m

                      a = g Sinθ      

Step 2:

Since each has the same initial velocity = 0

And have the same Sin ubiquitous acceleration.

For the time being, using the second movement equation of the Galileo,

                            S = ut + 1/2 × at²

                     S = 0 × t + 1/2 × g × sinθ*t²

From the above equation, to find t,

                              t² = 2S/gsinθ

                              t = √(2S/gsinθ)

Since there has to be a certain magnitude.

Thus, option (d) - all will achieve same kinetic energy.