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 tangential to path. Equation of path AB is `x^(2)=8y` and BC is straight line which tangent on curve AB to Point B (` mu` between block and path ABC is 0.5). Then value of `'lambda'` is `[g =10m//s^(2)]`

Explanation

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

Now, by `W_("net")=DeltaKE=0`
`W_(F)-mg (10+2)-mu mg(10+4)=0`
`rArr W_(F)=380=76xx5rArr lambda=5`