Home
Class 11
PHYSICS
The gravitational field in a region is g...

The gravitational field in a region is given by `vecE= - (10Nkg^-1)(veci+vecj)`. Find the work done by an external agent to slowly shift a particle of mass 2 kg from the point (0,0) to a point (5m,4m)`

Text Solution

Verified by Experts

As the particle is slowly shifted, its kinetic energy remains zero. The total work done on the particle is ths zero. The work done by the exterN/Al agent should be negative of the work done by th gravitatioN/Al field. The work done by the field is
`int_t^fvecF.vec(dr)` ltbr.gtConsider ure suppose the particle is taken from O to A and then from A to B. The force on the partivle is
`vecF=mvecE=(2kg)(10Nkg^-1)(veci+vecj)=(20N)(veci+vecj)`.

The work done by the field during the displacement OA is
`W_1=int_0^(5m) F_x dx`
`=int_0^(5m)(20N)dx=20Nx5m=100J`
Similarly the work done in displacement AB is
`W_2=int_0^(4m)F_ydy=int_0^(4m)(20N)dy`
`=(20N)(4m)=80J `
Thus,the total work doen by the field as the particle is shifted from O to B is 180 J.
Thework done work is independent of the path so that we can choose any path convenient to us O to B.
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    HC VERMA|Exercise Question for short Answers|19 Videos

  • GRAVITATION

    HC VERMA|Exercise Objective -1|17 Videos

  • GRAVITATION

    HC VERMA|Exercise Exercises|39 Videos

  • FRICTION

    HC VERMA|Exercise Exercises|31 Videos

  • HEAT AND TEMPERATURE

    HC VERMA|Exercise Exercise|34 Videos

Similar Questions

Explore conceptually related problems

The gravitational field in a region is given by vecE=(5Nkg^-1)veci+(12Nkg^-1)vecj. . find the magnitude of the gravitational force acting on a particle of mass 2 kg placed at the origin

The gravitational field in a region is given by E=(2veci+vecj)Nkg^-1 show that no work is done by the gravitational field when particle is move on the line 3y+2x=5 .

Find the ratio of the linear momenta of two particles of masses 1.0 kg and 4.0 kg if their kinetic energies are equal.

The electric field in a region is given by vecE=3/5 E_0veci+4/5E_0vecj with E_0=2.0 xx 10^3 N C^(-1) . Find the flux of this field through a recatngular surface of area 0.2m^2 parallel to the y-z plane.

Find the foot of the perpendicular drawn from the point (1,0, 3) to the join of points (4,7,1) and (3,5,3).

A bar magnet with magnetic moment 2.5 xx10^3 J T^(-1) is rotating in horizontal plane in thespacecontaining magnetic induction B = 4xx10^(-5) T. The work done in rotating the magnet slowly from a direction parallel to the field to a direction 45^@ from the field,is (in joule)

A particle having mass m and charge q is released from the origin in a region in which electric field and magnetic field are given by vecB =- B_0vecJ and vecE - E_0 vecK. Find the speed of the particle as a function of its z-coordinate.

Find the work done by the force F=3 hat i- hat j-2 hat k acting on a particle such that the particle is displaced from point A(-3,-4,1) and B(-1,-1,-2)dot

The two blocks in an Atwood machine have masses 2.0 kg and 3.0 kg. Find the work done by gravity during the fourth second after the system is released from rest.