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. `W_(1)gtW_(2)gtW_(3)`
B. `W_(1)=W_(2)=W_(3)`
C. `W_(1)ltW_(2)gtW_(3)`
D. `W_(2)gtW_(1)gtW_(3)`

Answer

B

Explanation

As gravitatonal force is a conservative force, work done is independent of path.
`:. W_(1)=W_(2)=W_(3)`