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

The position vector of a particle `vec(R )` as a funtion of time is given by:
`vec(R )= 4sin(2pit)hat(i)+4cos(2pit)hat(j)`
Where `R` is in meters, `t` is in seconds and `hat(i)` and `hat(j)` denote until vectors along x-and y- directions, respectively Which one of the following statements is wrong for the motion of particle ?

A

Path of the particle is a circle of radius 4 meter

B

Acceleration vector is along `- vec R`.

C

Magnitude of acceleration vector is `(v^(2))/(R )`,where v is the velocity of particle.

D

Magnitude of the velocity of aprticle is 8 meter/second

Text Solution

Verified by Experts

The correct Answer is:
D
`x=4 sin 2pit`
`y=4 cos 2pit`
`x^(2)+y^(2)=4^(2) (i)` is correct `(d^(2)R)/(dt^(2))[(4 sin 2 pit) hati+4 cos (2pit) hatj(2pi)^(2)]`
`=-(4pi^(2))barR:.(2)` is correct
(iii) is correct
`v=(dR)/(dr)=4(2pi)((cos 2pit) hati- sin (2pit)hatj)`
`|v|=pi`
`:.` Ans (4) is wrong
Promotional Banner

Similar Questions

Explore conceptually related problems

Position vector of a particle is expressed as function of time by equation vec(r)=2t^(2)+(3t-1) hat(j) +5hat(k) . Where r is in meters and t is in seconds.

The position vector of a particle moving in x-y plane is given by vec(r) = (A sinomegat)hat(i) + (A cosomegat)hat(j) then motion of the particle is :

The angle which the vector vec(A)=2hat(i)+3hat(j) makes with the y-axis, where hat(i) and hat(j) are unit vectors along x- and y-axis, respectively, is

A particle is moving with a position vector, vec(r)=[a_(0) sin (2pi t) hat(i)+a_(0) cos (2pi t) hat(j)] . Then -

The position of a particle at time moving in x-y plane is given by vec(r) = hat(i) + 2 hat(j) cos omegat . Then, the motikon of the paricle is :

The position of a particle at time moving in x-y plane is given by vec(r) = hat(i) + 2 hat(j) cos omegat . Then, the motikon of the paricle is :

The position vector of a particle changes with time according to the relation vec(r ) (t) = 15 t^(2) hat(i) + (4 - 20 t^(2)) hat(j) What is the magnitude of the acceleration at t = 1?

A particle is moving in a plane with velocity given by vec(u)=u_(0)hat(i)+(aomega cos omegat)hat(j) , where hat(i) and hat(j) are unit vectors along x and y axes respectively. If particle is at the origin at t=0 . Calculate the trajectory of the particle :-

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.