a stone is dropped from a height h. Its potential energy at a particular instant is nine times its kinetic energy. When the velocity of stone become double its velocity at that instant what will be the rario of its new kinetic
energy and new potential energy plz answer my question
Answers
Answer:
2/3
Explanation:
a stone is dropped from a height h. Its potential energy at a particular instant is nine times its kinetic energy. When the velocity of stone become double its velocity at that instant what will be the rario of its new kinetic
energy and new potential energy
Potential energy at height h = mgh
kinetic energy = (1/2)mv² = 0 ( as at rest)
Total energy = mgh
let say at T₁
potential energy is 9 times its kinetic energy
V = 0 + gT₁
kinetic energy = (1/2)m(gT₁)²
Potential energy = mgh - (1/2)m(gT₁)²
mgh - (1/2)m(gT₁)² = 9 * (1/2)m(gT₁)²
=> mgh = 5m(gT₁)²
=> h = 5gT₁²
=> gT₁² = h/5
Velocity = gT₁
Velocity become doubles = 2gT₁
Kinetic energy = (1/2)m(2gT₁)² = 2mg . gT₁² = 2mg (h/5) = (2/5) mgh
Potential energy = mgh - (2/5) mgh = (3/5) mgh
rario of its new kinetic energy and new potential energy = (2/5)mgh / (3/5) mgh
= 2/3