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A particle of mass m is dropped from a...

A particle of mass m is dropped from a height h above the ground. At the same time another particle of mass 2m is thrown vertically upwards from the ground with a speed of `sqrt(gh)` . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of `sqrt(h/g)` is :

A

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

B

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

C

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

D

(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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