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A particle of mass 2 is dropped from a h...

A particle of mass 2 is dropped from a height 80 m above the ground. At the same time another particle of mass m is thrown vertically upwards from the ground with a speed of 40 m/s. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of second is:

A

`((sqrt(112)-2)/(3))`

B

`((sqrt180 -2)/(3))`

C

`((sqrt105-2)/(5))`

D

`((sqrt112 + 2)/(5))`

Text Solution

Verified by Experts

The correct Answer is:
A
Particles will collide after time `t_(0) = (80)/(40)` = 2 sec.
at collision , `v_(A) = 20 " " v_B = - 20`
Velocity of combined mass `= (2 m xx 20-m xx 20)/(2m + m) = (20)/(3)` m/s
Time taken by combined mass to rach the ground Time `=((sqrt(112)-2)/(3))` sec.
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