question_answer

A body freely falling from rest has a velocity v after it falls through a distance h. The distance it has to fall down further, for its velocity to become double ...... is times h. (a) 4 h                                   (b) 3 h   (c) h                                       (d) 16 h

Answer:

Let v be the velocity acquired by the body when it travels h metre starting from rest. The distance it has to fall down further for its velocity to become double is given as with final velocity v and initial velocity equal to zero with final velocity 2v and initial velocity v after travelling h metre. \[{{v}^{2}}{{o}^{2}}=2gh\] \[{{v}^{2}}=2gh\]                                             .... (1) \[{{(2v)}^{2}}{{v}^{2}}=2g{{h}^{1}}\]                 \[3{{v}^{2}}=2g{{h}^{1}}\]                            ...(2) \[\frac{2}{4}=\frac{3{{v}^{2}}}{{{v}^{2}}}=\frac{2g{{h}^{1}}}{2gh}\]\[\Rightarrow \]\[{{h}^{1}}=3h\]