InterviewSolution
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InterviewSolution
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Three particles are projected vertically upward from a point on the surface of the earth with velocities `sqrt(2gR//3)` surface of the earth. The maximum heights attained are respectively `h_(1),h_(2),h_(3)`.A. `h_(1):h_(2)=2:3`B. `h_(2):h_(3)=3:4`C. `h_(1):h_(3)=1:4`D. `h_(2)=R` |
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Answer» Correct Answer - C::D Case: I `U_(i)+K_(f)=U_(f)+K_(g)` `(-Gm_(e)m)/(R)+(1)/(2)mv^(2)=-(GM_(e)m)/(R+h_(1))+0` `(-GM_(e)m)/(R)+(1)/(2)m(2GM_(e))/(R^(2))(R)/(3)=-(GM_(e)m)/(R+h_(1))` `-(1)/(R)+(1)/(3R)=-(1)/(R+h_(1))impliesh_(1)=(R)/(2)` Case II: `U_(i)+K_(i)=U_(f)+K_(g)` `-(GM_(e)m)/(R)+(1)/(2)mv^(2)=-(GM_(e)m)/(R+h_(2))+0` `(-GM_(e)m)/(R)+(1)/(2)m(2GM_(e))/(R^(2))R=-(GM_(e)m)/(R+h_(2))` `-(1)/(R)+(1)/(2R)=-(1)/(R+h_(2))impliesh_(2)=R` Case III: `U_(i)+K_(i)=U_(f)+K_(g)` `-(GM_(e)m)/(R)+(1)/(2)m(4GM_(e))/(R^(2))(R)/(3)=-(GM_(e)m)/(R+h_(3))` `-(1)/(R)+(1)/(3R)=-(1)/(R+h_(3))impliesh_(3)=2R` |
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