If `W_(1) W_(2)` and `W_(3)` represent the work done in moving a particle from `A` to `B` along three different paths `1.2` and`3` respectively (asshown ) in the gravitational fieled of a point mass m, find the correct relation between ` `W_(1) W_(2)` and `W_(3)`

Options

A. (a)`W_1 gt W_2 gt W_3`
B. (b)`W_1 = W_2 = W_3`
C. (c)`W_1 lt W_2 lt W_3`
D. (d)`W_2 lt W_1 lt W_3`

Answer

B

Explanation

Gravitational field is a conservative force field. In a conservative force field work done is path independent
`:. W_1 = W_2 = W_3`.