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A small particle of mass ` m` is projected at an angle `theta` with the ` x`- axis with an initial velocity ` v_(0)` in the ` x-y `plane as shown in the figure . At a time ` t lt ( v_(0) sin theta)/(g) `, the angular momentum of the particle is where `hat (i) , hat (j) and hat(k)` are unit vectors along `x , y and z` - axis respectively. A. ` - mg v_(0)t^(2) cos theta hat(j)`B. ` mg v_(0)t cos theta hat(k)`C. ` -1/2 mgv_(0)t^(2) cos theta hat(k)`D. `1/2 mg v_(0) t^(2) cos theta hat(i)` |
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Answer» Correct Answer - C ` vec(L) = m( vec ( R) xxvec(v) )` ` vec(L` = m [ v_(0) cos theta t hat(i) + ( v_(0) sin theta t - 1/2 gt^(2) ) hat (j) ] xx [ v_(0) cos theta hat (i) + ( v_(0) sin theta - gt ) hat (j) ] ` ` = m v_(0) cos theta t [ -1/2 gt ] hat (k) = -1/2 mgv_(0) cos theta hat (k) ` |
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