Home
Class 11
PHYSICS
A varable force, given by the 2- dimensi...

A varable force, given by the 2- dimensional vector`overlineF=(3xx^(2)hati+4 hatj),` acts on a particle. The force is in newton and x is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates (2,3) to (3,0) (The coornates are in metres)

A

`-7 J`

B

zero

C

`+7 J`

D

`+19 J`

Text Solution

Verified by Experts

The correct Answer is:
C
`vecF=3x^2 hati+4hatj`
`vecr=xhati+yhati " " therefore " " dvecr=dxhati+dyhatj`
Work done , `W=int vecF.dvecr`
`=underset("(2,3)")overset("(3,0)")int(3x^2 hati+ 4hatj).(dx hati+dyhatj)`
`=underset("(2,3)")overset("(3,0)")int3x^2 dx+4dy=underset("(2,3)")overset("(3,0)")intd(x^3+4y)`
`=[x^3+4y]_("(2,3)")^("(3,0)")=3^3+4xx0-(2^3 + 4 xx 3)`
=27+0-(8+12)=27-20= +7 J
According to work- energy theroem,
Change in the kinetic energy = Work done , W = +7 J
Promotional Banner

Topper's Solved these Questions

  • WORK , ENERGY AND POWER

    NCERT FINGERTIPS|Exercise The Concept Of Potential Energy|9 Videos

  • WORK , ENERGY AND POWER

    NCERT FINGERTIPS|Exercise The Conservation Of Mechanical Energy|12 Videos

  • WORK , ENERGY AND POWER

    NCERT FINGERTIPS|Exercise Work Done By A Variable Force|3 Videos

  • WAVES

    NCERT FINGERTIPS|Exercise Assertion And Reason|15 Videos

Similar Questions

Explore conceptually related problems

A force acting on particle is given by vecF=(3x^2hati+4yhatj)N . The change in kinetic energy of particle as it moves from (0,2m) to (1m,3m) is

Force F=[3x^2hati+4hatj] N where , x in metres, acts on a particle. How much work is done on the particle as it moves from coordinates (2m,3m) to (3m, 0m)?

A force F = 0.5x + 10 acts on a particle. Here F is in newton and x is in metre. Calculate the work done by the force during the displacement of the particle from x = 0 to x = 2 metre.

A force (hati-2hatj+3hatk) acts on a particle lying at origin. What is the torque acting on the particle.

A force F=(3xhati+4hatj) Newton (where x is in metres) acts on a particle which moves from a position (2m, 3m) to (3m, 0m). Then the work done is

A force (hati-2hatj+3hatk) acts on a particle of positive vector (3hati+2hatj+hatk) . Calculat the torque acting on the particle.

A force vecF=(3xN)hati+(4N)hatj , with x in meter, acts on a particle, changing only the kinetic energy of the particle. How mcuh work is done on the particle as it moves from coordinates (2m, 3m, 5m) to (3m, 0m, 6m) ? Does the speed of the particle increase, decrease, or remain the same?

A force F=(15+0.50x) acts on a particle in the X-direction ,where F is in newton and x in metre Find the work done ' by this force during a displacement from x=0 to x=2.0 m .

Kinetic energy of a particle moving in a straight line varies with time t as K = 4t^(2) . The force acting on the particle