A particle moves along the X-axis x=0 to x=5 m under the influence of a force given by `F=10-2x+3x^(2)`. Work done in the process is

Answer

[(A – P, Q, R, T); (B – Q, S) (C – P, Q, R, S) (D – P, R, T)]

Explanation

The particle will experience an attractive force towards x = 0 in the region `| x | < a`
If `0 < x < a implies F = -ve and if x > a implies F = + ve`
The particle will oscillate about `x = -a` if U is min at `x = -a` and U at `x = -a < (U_0)/4`
Also `F = (-d U)/(dx)`
`implies (A) F= (2 U_0x)/(a^2)[1 - (x/a)^2] " "(B) F = -(U_0x)/(a^2)`
`(C ) F = - (U_0x)/(a^2)(1 - (x^2)/a^2))e^((-x^2)/(a^2)) " "(D) F = - (U_0)/(2a) (1 - x^2)/(a^2))` .