Home
Class 11
PHYSICS
A body is displaced from prigin to (1m,1...

A body is displaced from prigin to (1m,1m) by force
`F=(2yhati + 3x^(2)hatj)` along two paths
(a) `x=y` (b) `y=x^(2)`
Find the work done along both paths.

Text Solution

Verified by Experts

`F=(2yhati + 3x^(2)hatj)`
`dr=(dxhati + dyhatj)`
`F.dr=(2ydx + 3x^(2)dy)`
We cannot integrate F.dr or `(2ydx + 3x^(2)dy)` as such to find the work done. But along the given paths we can change this expression.
(a) Along the path `x = y`
`(2y dx + 3x^(2)dy) = (2x dx + 3y^(2)dy)`
`W_(1) = int_(0,0)^(1m,1m,)F.dr =int_(0,0)^(1m,1m)(2xdx + 3y^(2)dy)`
`=[x^(2) + y^(3)] _(0,0)^(1m,1m)`
`=(1)^(2) + (1)^(3)=2J`
(b) Along the path `y=x^(2)`
`(2ydx + 3x^(2)dy) =(2x^(2)dx + 3ydy)`
`:. W=(2)=int_(0,0)^(1m,1m)F.df =int(2x^(2)dx + 3y dy)`
`=[2/3x^3 + 3/2y^(2)]_(0,0)^(1m,1m)`
`=(13)/6 J`
Promotional Banner

Topper's Solved these Questions

  • WORK, ENERGY & POWER

    DC PANDEY|Exercise TYPE2|1 Videos

  • WORK, ENERGY & POWER

    DC PANDEY|Exercise Miscellaneous Example|6 Videos

  • WORK, ENERGY & POWER

    DC PANDEY|Exercise Level 2 Comprehension Based|2 Videos

  • WAVE MOTION

    DC PANDEY|Exercise Integer Type Question|11 Videos

  • WORK, ENERGY AND POWER

    DC PANDEY|Exercise MEDICAL ENTRACES GALLERY|33 Videos

Similar Questions

Explore conceptually related problems

A body is desplaced from origin to (2m, 4m) under the following two forces: (a) F=(2^hati + 6^hatj)N , a constant force (b) F(2x^hati + 3y^(2)hatj)N Find word done by the given forces in both cases.

An object is displaced from point A(2m,3m,4m) to a point B(1 m,2 m,3 m) under a constant force F=(2hati + 3hatj + 4hatk)N . Find the work done by this force in this process.

A body is displaced from (0,0) to (1 m, 1m) along the path x = y by a force F=(x^(2) hatj + y hati)N . The work done by this force will be

An object is displaced from a point A(0, 0, 0) to B(1m, 1m , 1m) under a force vecF=(yhati+xhatj)N . Find the work done by this force in this process.

An object is displaced from positin vector r_1=(2hati+3hatj) m to r_2=(4hati+6hatj) m under a forc F=(3x^2hati+2yhatj)N Find the work done by this force.

A particle is moved from (0,0) to (a,a) under a force bar F = (3hati + 4hatj) and path 2is OQP .Let W_(1) and W_(2) be the work by done this force in these to paths .Then .

A block is displaced from (1m, 4m, 6m) to (2hati+3hatj-4hatk) m under a constant force F=(6hati-2hatj + hatk) N . Find the work done by this force.

A particle is movbed from (0, 0) to (a, a) under a force F =(x^(2)hati+y^(3)hatj) from two paths. Path 1 si OP and Path 2 is OQP . Let W_(1) and W_(2) be the work done by this force in these two paths. Then

A body displaced from (1,1) to (2,2) along the line y=x under the force vecF=xhat(j)+yhat(i) then find the work done by this force for above displacement. (all units are in S.I.)

Due to a force of (6hati+2hatj)N the displacement of a body is (3hati-hatj)m , then the work done is