question_answer

A particle slides on a frictionless elevated curved track from a point A, which terminates in a straight horizontal section ending at C, as shown. If the particle looses the contact with the track at 0, the particle will hit the ground from C at a horizontal distance of:

A)  \[0.5m\]                      

B)  \[0.8m\]

C)  \[1.0m\]                      

D)  \[1.2m\]

Correct Answer: C

Solution :

From work - energy theorem Loss in potential energy= Gain in Kinetic energy Gives,    \[u=\sqrt{2g({{h}_{1}}-{{h}_{2}})}\] \[\therefore \] Range, \[R=u\sqrt{\frac{2{{h}_{2}}}{g}}=2\sqrt{{{h}_{2}}({{h}_{1}}-{{h}_{2}})}\]                                 \[\left( as,\,t=\sqrt{\frac{2H}{g}} \right)\]                 \[R=2\sqrt{0.5\times 0.5}=1.0m\]