Question

An object released from certain height h, from the ground rebounds to a height h/4after striking the ground. The fraction of the energy lost by it is

• A. $\frac 1{4} $
• B. $\frac 3{4} $
• C. $\frac 1{2} $
• D. $\frac 1{8} $
• E. $\frac 3{8} $

Answer 1

The Correct Option is B

We are given that an object is released from a certain height \( h \), and after striking the ground, it rebounds to a height of \( \frac{h}{4} \). We need to find the fraction of energy lost by the object during the rebound. 

The total mechanical energy of the object is initially in the form of potential energy when it is at height \( h \). The potential energy \( E_{\text{initial}} \) at height \( h \) is given by: \[ E_{\text{initial}} = mgh \] After the rebound, the object reaches a height of \( \frac{h}{4} \). The potential energy \( E_{\text{final}} \) at this new height is: \[ E_{\text{final}} = mg \times \frac{h}{4} = \frac{mgh}{4} \] The energy lost is the difference between the initial and final energies: \[ \text{Energy lost} = E_{\text{initial}} - E_{\text{final}} = mgh - \frac{mgh}{4} = \frac{3mgh}{4} \] The fraction of the energy lost is: \[ \text{Fraction of energy lost} = \frac{\text{Energy lost}}{\text{Initial energy}} = \frac{\frac{3mgh}{4}}{mgh} = \frac{3}{4} \]

Correct Answer:

Correct Answer: (B) \( \frac{3}{4} \)