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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

`(sqrt40-2)/6`

B

`(sqrt30-3)/7`

C

`(sqrt20-2)/5`

D

`sqrt(3/2)`

Text Solution

Verified by Experts

The correct Answer is:
A

Particles will collide after time `t_0 = (h)/(sqrt(gh)) `
at collision , `v_A = "gt"_0 " "v_B = u_B - "gt"_0`
`implies v_A = - gsqrt(h//g), v_B = 0 `
Time taken by combined mass to reach the ground
Time `= ((sqrt(40)-2)/(6)) sqrt(h//g)`
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