Work done by force F to move block of mass `2 kg ` from A to C very slowly is `(76 lambda)J`. Force F is always acting tengetial to path. Equation of path AB is `x^(2)=8y` and BC is straight line which is tengent on curve AB at point B (`mu` between block and path ABC is 0.5). then value of `lambda` is `[g=10 m//s^(2)]`

Explanation

Slope of line `BC = (dy)/(dx) =(2x)/(8)=(2 xx4)/(8)=1`
`rArr theta = 45^(@)`

If the mass m is taken from A to C slowly work done by friction will always be equal to the `W_(r) = mu mg x`

Now, by `W_("net") = Delta KE =0`
`W_(F)-mg(10+2)-mu mg(10+4)=0`
`rArr W_(F) = 380 = 76 xx 5`
`rArr lamda = 5`