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A particle of mass `5kg` moving in the `X-Y` plane has its potential energy given by `U=(-7x+24y) J`. The particle is initially at origin and has a velocity `vec(U)=(14.4+4.2J)m//s`A. The particle has speed `20 m//s` at `t=4` secB. The particle has an acceleration `25 m//s^(2)`C. The acceleration of particle is normal to its intial velocity.D. None of the above each correct |
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Answer» Correct Answer - C Force acting on the particle `vec(F)=-(delU)/(delx)hat(i)-(delU)/(dely)hat(j)=7hat(i)-24hat(j)` Accerleration of particle `=(F)/(m)=sqrt(7^(2)+24^(2))/(5)=(25)/(5)=5ms^(-2)` velocity of particle `vec(v)=vec(u)+vec(a)t=(14.4hat(i)+4.2hat(j))+(1.4hat(i)-4.8hat(j))t` Speed at `4` sec`=sqrt((14.4+5.6)^(2)+(19.2-4.2)^(2))` `=25ms^(-1)` Now `vec(a).vec(u)=(1.4hat(i)-4.8hat(j)).(14.4hat(i)+4.2hat(j))=20.16-20.16=0rArr` The acceleration of particle is normal to its initial velocity. |
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