A particle of mass m m

Question -

A particle of mass m moves on the `x`-axis under the influence of a force of attraction towards the origin O given by

`F = - k/x^2``vec(i)`. If the particle starts from rest at `x` = a . The speed it will attain to reach at distance `x` from the origin O will be .

Options:

A . `sqrt(2k)/m [(x - a)/(ax)]^(1/2)`

B . `sqrt(2k)/m [(a + k)/(ax)]^(1/2)`

C . `sqrt(k)/m [(ax)/(x - a)]^(1/2)`

D . `sqrt(m)/2k [(a - x)/(ax)]^(1/2)`

Answer: Option A

`because` `F = k/x^2`

`:.` Acceleration `int = - (k)/(mx^2)`

when `x` secreases , v increases

`:.` `int = - v (dv)/(dx)`

`:.` ` - v (dv)/(dx) = (k)/(mx^2)`

or `int_0^v vdv = k/m int_a^x 1/x^2 dx`

`:.` v = `sqrt(2k)/m [(x - a)/(ax)]^(1/2)`

Was this answer helpful ?

Next Question