Question

can someone answer this​

Answer 1

Slope = fo/xo

Eq = F - fo = fo/xo. ( x - 2xo)

F = m v dv/dx

F = fo/xo. ( x - 2xo) + fo)

Fdx = m v dv

integrate

fo/xo ( x^2/2 - 2xo x) + fo x = m v^2/2 + c

V at xo = √2 fo xo/m

fo/xo ( xo^2/2. - 2 xo^2) + fo xo = fo^2 xo^2/m + c

fo /xo ( -3/2. xo^2) + fo xo - fo^2 xo^2/m = c

- 3/2 fo xo + fo xo - fo^2 xo^2 /m = c

- fo xo/2 - fo ^2 xo^2/m = c

-fo xo ( 1/2 + fo xo/m) = c

Now put x= 4 xo

fo/xo ( 16 xo^2/2 - 8 xo^2) + 4 fo xo = mv^2/2 - foxo ( 1/2 + fo xo/m)

4 fo xo+ foxo ( 1/2 + foxo/m) = mv^2/2

4 foxo + foxo /2 + fo^2 xo^2 /m = mv^2/2

9/2. foxo + fo^2 xo^2/m = m v^2/2

9 foxo + 2 fo^2 xo^2/m= mv^2

9 fo xo/m + 2 fo^2 xo^2 /m^2 = v^2

(√2 fo xo /m. + 9/2√2)^2 - 81/8 = v^2

2√2 fo xo/m + 81/8 - 81/8 = v^2( assuming 1/√2 to be small) ,exonents multiplied when small

V= 2√( √2 foxo/m)

So (A)