Question

A sphere of radius 2mm and of density 7.5 × 10³ kg m^-3 falls from a height of 500m above the ground. Due to air resistance, its acceleration gradually decreases and becomes zero when it drops to half its original height. The drop then falls with a uniform terminal velocity. What is the work done by the gravitational force during the first and second half of its Journey?

Answer 1

Even though the resultant force acting on the sphere is different during the first and second half of its journey, the force due to gravity remains constant throughout and is equal to the weight of the sphere. The amount of work done during the first half is given by,

W = mgh where m is the mass of the body.

But m =\(\frac{4}{3}\)πr³d and h = \(\frac{500}{2}\)= 250m

W = \(\frac{4π}{3}\)(2 x 10^-3 )³ × 7.5 × 10³ × 9.8 × 250

= 4\(\frac{4π}{3}\)(2)³ × 7.5 × 9.8 × 250 × 10^-6 J

= 615.4 × 10^-3 = 0.615J

The work done remains the same during both the halves.