A stone is projected vertically upward to reach maximum height h. The ratio of its kinetic energy to its potential energy at a height (4/5) h, will be

Question

A stone is projected vertically upward to reach maximum height h. The ratio of its kinetic energy to its potential energy at a height (4/5) h, will be (A) 5:4 (B) 4:5 (C) 1:4 (D) 4:1

Tardigrade Admin · Accepted Answer

At a height (4/5) h, textPotential energy = textmg × (4 h /5) = (4/5) textmgh Total energy = mgh ∴ textK E at that height = textmgh - (4/5) mgh = (1/5) mgh â¡ ∴ textAt a height (4/5) h , â¡ textthe ratio of ( textKE/ textPE) = ((1/5) textmgh/(4)5 textmgh) = (1/4)

Q. A stone is projected vertically upward to reach maximum height h. The ratio of its kinetic energy to its potential energy at a height $\frac{4}{5} h,$ will be

$5 : 4$

$4 : 5$

$1 : 4$

$4 : 1$

At a height $\frac{4}{5} h,$
$Potential energy = mg \times \frac{4 h}{5} = \frac{4}{5} mgh$
Total energy = mgh
$∴ K E at that height = mgh - \frac{4}{5} m g h = \frac{1}{5} m g h$
$∴ At a height \frac{4}{5} h, the ratio of$
$\frac{KE}{PE} = \frac{\frac{1}{5} mgh}{\frac{4}{5} mgh} = \frac{1}{4}$

Q. A stone is projected vertically upward to reach maximum height h. The ratio of its kinetic energy to its potential energy at a height 54​h, will be

5:4

4:5

1:4

4:1