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Kasturba Jhaveri
Asked: 2022-11-07T22:33:53+05:30 In:

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. `A omega hat(i)`
B. `A omega hat(j)`
C. `A omega(hat(i)+hat(j))`
D. `A omega (hat(i)-hat(j))`

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. `A omega hat(i)`
B. `A omega hat(j)`
C. `A omega(hat(i)+hat(j))`
D. `A omega (hat(i)-hat(j))`
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1 Answer

  1. Correct Answer – B
    Substituting `vec(r )=(A cos omega t hat(i)+A sin omega t hat(j))`
    in `vec(v)= (dvec(r ))/(dt)` we have `vec(v) = A(d)/(dt)(cos omega t)hat(i)+A(d)/(dt)(sin omega t)hat(j)`
    `= – A omega sin omega t hat(i)+A omega cos omega t hat(j)`
    At `t = 0 , v= – A omega sin 0 hat(i)+A omega cos 0hat(j)= A omegahat(j)`

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