Read the following statements and choose the correct answer.
a) For a freely falling body the average velocity is proportional to square root of height of fall.
b) For a freely falling body the displacements in successive equal time intervals are in the ratio 1:4:9: .....
c) For a vertically projected body the displacement during last second of time of flight changes with velocity of projection.
d) For a body projected from the top of the tower the displacement of the body is negative when the body crosses the point of projection.

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a, c, d are true

both a, b are true

b & c are true

c and d are true

answer is A.

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Detailed Solution

a) Average velocity is given by V_avg = H/t = $\frac{H}{\sqrt{2 H / g}}$ = $\sqrt{g H / 2}$

b)S_n= g(n-1/2). Thus, ratio of successive intervals will be 1:3:5...

c)Displacement for last second of time of flight for a vertically projected body is given by

S = ut+1/2gt²

S_{last second} = v_lastsecond.(2u/g-1) + 1/2g(2u/g - 1)²

Thus, displacement varies with the velocity of projection.

d) For a body projected from the top of the tower will be moving downwards when it crosses the point again. Therefore displacement is negative.

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