A stone is projected vertically to reach a maximum height 'h'. The ratio of kinetic energy to potential energy at a height 4h/5 is

1) 5:4
2) 4:5
3) 1:4
4) 4:1

C)1:4

1:4

To determine the ratio of kinetic energy to potential energy at a height of 4h/5, we first need to understand the concepts of kinetic energy and potential energy.

The kinetic energy of an object is given by the formula: K.E. = 1/2 * m * v^2, where m denotes the mass of the object and v represents its velocity.

The potential energy of an object at a height 'h' is given by the formula: P.E. = m * g * h, where m denotes the mass of the object and g represents the acceleration due to gravity.

In this case, the stone is projected vertically, which means its initial velocity is zero. Therefore, at the maximum height 'h', the stone will momentarily come to a stop before coming back down.

At the maximum height 'h', the stone has no kinetic energy since its velocity is zero. Thus, the kinetic energy is zero.

At a height of 4h/5, the stone still has potential energy given by: P.E. = m * g * (4h/5)

Now, to calculate the ratio of kinetic energy to potential energy at this height, we need to divide the kinetic energy by the potential energy:

K.E. / P.E. = 0 / (m * g * (4h/5)) = 0

Therefore, the ratio of kinetic energy to potential energy at a height of 4h/5 is 0:1, which simplifies to 0:1.

None of the given answer options matches this ratio (0:1). Hence, none of the options provided in the question is correct.

At height 4h/5,

KE=h/5
PE=4h/5
Ratio of KE:PE=?