A particle is moving with momentum P and kinetic K in a gravity free space. A constant force F (directed perpendicular to the initial momentum) now ac

Question

A particle is moving with momentum P and kinetic K in a gravity free space. A constant force F (directed perpendicular to the initial momentum) now ac

A particle is moving with momentum P and kinetic K in a gravity free space. A constant force F (directed perpendicular to the initial momentum) now acts on the particle for time t. Final kinetic energy of the particle will be
A. `K [1 + ((Ft)/(P))^(2)]`
B. `K [1 + 2 ((Ft)/(2))^(2)]`
C. `K sqrt(1 + ((Ft)/(P))^(2))`
D. `K sqrt(1 + ((Ft)/(P))^(4))`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A
`a_(t) = (F)/(m)`
Integrating, we get `v_(t) = (F)/(m) t`
As `(p^(2))/(2m) = K :. V_(t) = (F)/(p^(2)) xx 2 Kt`
Now, `K_(f) = (1)/(2) mv^(2) = (1)/(2) m ((f^(2)4K^(2)t^(2))/(p^(4)) + v^(2))`
`= (2F^(2)K^(2)t^(2)m)/(p^(4)) + K = K [(2KF^(2)t^(2)m)/(p^(2)) + 1]`
`= K [1 + (2m)/(p^(2) xx p^(2)) xx (F^(2)t^(2))/(p^(2))]`