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Q.

A body of mass m is projected horizontally with a velocity v from the top of a tower of height h and it reaches the ground at a distance x from the foot of the tower. If a second body of mass 2m is projected horizontally from the top of a tower of height 2 h, it reaches the ground at a distance 2 x from the foot of the tower. The horizontal velocity of second body is

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a

v

b

2 v

c

2v

d

v/2

answer is C.

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Detailed Solution

For first body,       h=12gt2      …(1)and    x = vt         ….. (2)From eqs. (1) and (2),     h=12gx2/v2          ….(3)For second body, let v' be the velocity of projection, then2h=12g(2x)2v′2      …. (4)Dividing eq. (3) by eq. (4), we get12=x2v2×v′24x2  or  v′=2⋅v
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