InterviewSolution
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InterviewSolution
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The position vector `vacr` of the z-component of `vecL` is `55ma^2omega`. Following equation `vacr(t)= alphat^3hati+beta^2hatj,` where `alpha = 10//3ms^(-3), beta = 5 ms^(-2)` and m = 0.1kg. At t=1s, which of the following statement (s) is (are) true about the particle?A. The velocity `vacv` is given by `vacv = (10hati+10hatj) ms^(-1)`B. The angular momentum `vacL` with respect to the origin is given by `vacL = -5//3) hatk N ms.`C. The force `vacF` is given by `vacF = (hati+2hatj)ND. The torque `vactau` with respect to the origin is given by `vactau = -(20//3) hatk Nm` |
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Answer» Correct Answer - A::B (a,b) `vecr = alpha t^3 + betat^2 hatj` `vecr = (10)/(3) t^3 hati + 5t^2 hatjm` `vecv = (dvecr)/(dt) = 10t^2 hati + 10thatj ms^(-1)` `vecalpha = (dvecv)/(dt) = 20t hatj + 10hatjms^(-2)` At t = 1s `vecr_(t=1) = (10)/(3)hat I + 5hatjm` `vecv_(t =1) = 10hati + 10hatj ms^(-1)` `hatP_(t =1) = hati + hatj kgms^(-1)` `alpha_(t =1) = 20hati + 10 hatj ms^(-2)` `vecL = vecrxxvecP = |(hat i,hat j,hat k ),(10/3,5,0),(1,1,0)| = hatk[(10)/(3) -5]=-5/3 hatk kgms^(-1)` `vecF = mveca = (2hati + hatj)N` `vectau = vecrxxvecF=|(hat i,hat j,hat k ),(10/3,5,0),(2,1,0)|=hatk[(10)/(3) -10]=(-20)/(3) hatkN-m.` |
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