Question

A stone is projected vertically up to reach maximum height 'h'. The ratio of its kinetic energy to p.e., at a height 4/5h will be
A) 5:4
B) 4:5
C) 1:4
D) 4:1​

Answer 1

Answer:

Total Mechanical Energy remains same throughout the system:

Mechanical Energy = Potential Energy + Kinetic energy ( u=0)

ME= PE + KE

ME = mgh+1/2mv²

ME= mgh + 1/2m(u)²

ME = mgh + 1/2m(0)²

ME = mgh + 0

ME = mgh throughout the system

at height 4/5h: ME = mgh

mgh = mg(4/5)h

mgh = (4/5)mgh

KE = 1/2mv²

[v²= u² + 2aS]

[v² = (0)² + 2gh]

[v²=2gh]

now, KE = 1/2m(2gh)

KE= 1/2×m×2×g×(4/5)h

KE = (4/5)mgh

KE:PE = 4/5(mgh):4/5(mgh)

= 4/5:4/5

= 1:1