Home
Class 11
PHYSICS
The position vector of a particle is r =...

The position vector of a particle is `r = a sin omega t hati +a cos omega t hatj`
The velocity of the particle is

A

parallel to positive vector

B

perpendicular to position vector

C

directed towards the origin

D

directed away from the origin

Text Solution

Verified by Experts

The correct Answer is:
B
`vecr= (a cos omegat) hati + ( a sin omegat)hatj`
`(dvecr)/(dt) = vecv =- a omegasin omegat hati + aomega cos omegathatj`
`because" " vecr. vecv= 0`
`So, vecr" ""is" bot "to "vecv`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    GRB PUBLICATION|Exercise MORE THAN ONE CHOICE IS CORRECT|15 Videos

  • VECTORS

    GRB PUBLICATION|Exercise ASSERTION- REASON|1 Videos

  • VECTORS

    GRB PUBLICATION|Exercise PROBLEMS FOR PARCTICE|23 Videos

  • UNITS AND DIMENSIONS

    GRB PUBLICATION|Exercise Link Compression|6 Videos

Similar Questions

Explore conceptually related problems

The position vector of a particle is vec( r) = a cos omega t i + a sin omega t j , the velocity of the particle is

The position vectors os a particle is r=(acosomegat)hati+(aomegat)hatj. The velocity of particle is

The motion of a particle is given x = A sin omega t + B cos omega t The motion of the particle is

The motion of a particle is given by x = A sin omega t + B os omega t . The motion of the particle is

Position vector of a particle moving in x-y plane at time t is r=a(1- cos omega t)hat(i)+a sin omega t hat(j) . The path of the particle is

The position vector of a particle is given by vec(r ) = k cos omega hat(i) + k sin omega hat(j) = x hat(i) + yhat(j) , where k and omega are constants and t time. Find the angle between the position vector and the velocity vector. Also determine the trajectory of the particle.

A particle moves so that its position vector varies with time as vec(r )= A cos omegathat(i)+A sin omega t hai(j) . The initial velocity of the particel the particle is

A x and y co-ordinates of a particle are x=A sin (omega t) and y = A sin(omegat + pi//2) . Then, the motion of the particle is

GRB PUBLICATION-VECTORS-OBJECTIVE QUESTIONS
  1. A vector vecF(1) is along the positive X-axis. If its vectors product ...

    Text Solution

    |

  2. The torque of the force vecF=(2hati-3hatj+4hatk)N acting at the point ...

    Text Solution

    |

  3. The position vector of a particle is r = a sin omega t hati +a cos ome...

    Text Solution

    |

  4. The angle made by the vector 4hati - 3hatj + 5hatk with z-axis is :

    Text Solution

    |

  5. Three vectors veca,vecb and vecc satisfy the relation veca.vecb=0 and ...

    Text Solution

    |

  6. The resultant of two forces , one double the other in magnitude is pe...

    Text Solution

    |

  7. The value of n so that vectors 2hati+3hatj-2hatk, 5hati+nhatj+hatk and...

    Text Solution

    |

  8. A projectile of mass m is fired with a velocity v from point P at an a...

    Text Solution

    |

  9. Magnitudes of four pairs of displacement vectors are given. Which ...

    Text Solution

    |

  10. Two forces of magnitudes 30, 60 and P newton acting at a point a...

    Text Solution

    |

  11. A force F=ahati+bhatj+chatk is acted upon a body of mass m. If the bod...

    Text Solution

    |

  12. Let vecF be a force acting on a particle having positon vector vecr. L...

    Text Solution

    |

  13. If |vecA xx vecB| = sqrt(3) vecA .vecB then the value of |vecA xx ve...

    Text Solution

    |

  14. vecA, vecB and vecC are vectosrs each having a unit magneitude. If ...

    Text Solution

    |

  15. Three forces act on a body. The body will certainly have an accele...

    Text Solution

    |

  16. If the sum and difference of two vectors are at right angles, show tha...

    Text Solution

    |

  17. Vectors vecA and vecB are mutually perpendicular . Component of vecA...

    Text Solution

    |

  18. For a particle in uniform circular motion , the acceleration vec(a) a...

    Text Solution

    |

  19. A particle is given successive displacments. Which of the followin...

    Text Solution

    |

  20. An expression which cannot be defined meaningfully among vectors is :

    Text Solution

    |