CBSE Class 12-science Answered

Consider a simple pendulum:

When the pendulum is given a small push, to start it swinging, the pendulum bob would continue to revolve continuously forever, in a vertical circle, (assuming the right sort of pivot), if it were not for the effects of gravity and friction. The restoring force, which makes the pendulum swing to and fro, is the force of gravity acting on the bob. When one calculates the formula for the periodic time of swing of the pendulum, one finds that the periodic time depends not only on the length of the pendulum and the acceleration due to gravity, but also on the ratio of thegravitational mass of the bob to its inertial mass. However, whatever material is chosen for the bob, this ratio is always found to be unity. Hence, experimentshows that the gravitational mass of any given body is equal to its inertial mass.

2.

f the energy of motion (kinetic energy) of a projectile just equals the pull of gravitational (potential) energy, the projectile can barely escape the Earth.

Notice that the mass of the projectile can cancel on both sides of the equation. This is why the escape velocity is independent of the mass of the projectile.

vesc = sqrt(2GM/r)