A ball of mass m is dropped from a certain height h on a sand floor. If the ball penetrates 'x' meters into the sand, the average resistive force offered by sand on the ball is:
Correct answer: B. mg (h/x)
- A. mg (x/h)
- B. mg (h/x)
- C. mg (1+h/x)
- D. mg (1 - h/x)
- E. mgh + mgd
Explanation
The work done by the resistive force of sand is given by:W = Fd = (1/2) kx2where F is the average resistive force offered by the sand on the ball, d is the distance penetrated by the ball, and k is a constant that depends on the sand properties.At the maximum depth, all the potential energy of the ball is converted into the work done by the resistive force of sand, so we can write:mgh = (1/2) kx2Solving for k, we get:k = 2mgh/x2Now, the average resistive force offered by the sand on the ball is:F = kx/2 = mgh/xTherefore, the correct answer is B) mg(h/x).
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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