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

The position vector of a particle is `vec( r ) = ( 3 hat( i ) + 4 hat( j ))` metre and its angular velocity ` vec( omega) =(hat( j)+ 2hat( k )) rad s^(-1)` then its linear velocity is ( in `ms^(-1)`)

A

`(8hat(i)-6hat(j)+3hat(k))`

B

`(3hat(i)+6hat(j)+8hat(k))`

C

`-(3hat(i)+6hat(j)+6hat(k))`

D

`(6hat(i)+8hat(j)+3hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(v)=vec(omega)xx vec(r )=(3hat(i)+4hat(j)+0hat(k))xx (0 hat(i)+hat(j)+2hat(k))=|(hat(i),hat(j),hat(k)),(3,4,0),(0,1,2)|=8hat(i)-6hat(j)+3hat(k)`.
Promotional Banner

Topper's Solved these Questions

  • ROTATIONAL MOTION

    ERRORLESS |Exercise Practice Problems (Problems based on centre of mass)|12 Videos

  • ROTATIONAL MOTION

    ERRORLESS |Exercise Practice Problems (Problems based on angular displacement, velocity and acceleration)|16 Videos

  • NEWTONS LAWS OF MOTION

    ERRORLESS |Exercise Self Evaluation Test|16 Videos

  • SIMPLE HARMONIC MOTION

    ERRORLESS |Exercise simple Harmonic Motion|21 Videos

Similar Questions

Explore conceptually related problems

The position of a particle is given by vec r = hat i + 2hat j - hat k and its momentum is vec p = 3 hat i + 4 hat j - 2 hat k . The angular momentum is perpendicular to

For a body, angular velocity (vec(omega)) = hat(i) - 2hat(j) + 3hat(k) and radius vector (vec(r )) = hat(i) + hat(j) + vec(k) , then its velocity is :

What is the value of linear velocity, if vec(omega) = 3hat(i)-4 hat(j) + hat(k) and vec(r) = 5hat(i)-6hat(j)+6hat(k)

Two particles having position vectors vec(r )_(1) = ( 3 hat(i) + 5 hat(j)) meters and vec( r)_(2) = (- 5 hat(i) - 3 hat(j)) metres are moving with velocities vec(v)_(1) = ( 4 hat(i) + 3 hat(j)) m//s and vec(v)_(2) = (alpha hat(i) + 7 hat(j)) m//s . If they collide after 2 s , the value of alpha is

What is the value of linear velocity. If vec(omega)=3hat(i)-4hat(j)+hat(k)and vec(r)=5hat(i)-6hat(j)+6hat(k) ?

The angular velocity of a rotating body is vec omega = 4 hat i + hat j - 2 hat k . The linear velocity of the body whose position vector 2hati + 3 hat j - 3 hat k 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.

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

The velocity of a particle of mass m is vec(v) = 5 hat(i) + 4 hat(j) + 6 hat(k)" " "when at" " " vec(r) = - 2 hat(i) + 4 hat (j) + 6 hat(k). The angular momentum of the particle about the origin is