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

A particle of mass 2m 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

`((sqrt(80) - 2)/(3))`

C

`((sqrt(105) - 2)/(5))`

D

`((sqrt(112) + 2)/(5))`

Text Solution

Verified by Experts

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