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  4. A body is thrown vertically up with certain initial velocity. The potential and kinetic energies of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of potential and kinetic energies of the body when it crosses the same point, is

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Q. A body is thrown vertically up with certain initial velocity. The potential and kinetic energies of the body are equal at a point $P$ in its path. If the same body is thrown with double the velocity upwards, the ratio of potential and kinetic energies of the body when it crosses the same point, is

Punjab PMETPunjab PMET 2008Work, Energy and Power

Solution:

Let a point where, $\frac{1}{2} mv ^{2}= mgh$
Total M.E $=2 mgh$
Now, when v is twice
Total M.E $=8 mgh$
Now when the ball passes through that point
$K . E =8 mgh - mgh =7 mgh$
$P \cdot E=m g h$
P.E : K.E $=1: 7$

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