AP EAMCET · PHYSICS · Motion In One Dimension

A particle is released from a height $H$ . At a certain height its kinetic energy is half of its potential energy with reference to the surface of the earth. Height and speed of the particle at that instant are respectively

A $\frac{H}{3}, \sqrt{\frac{2 g H}{3}}$
B $\frac{H}{3}, 2 \sqrt{\frac{g H}{3}}$
C $\frac{2 H}{3}, \sqrt{2 g H}$
D $\frac{2 H}{3}, \sqrt{\frac{2 g H}{3}}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{2 H}{3}, \sqrt{\frac{2 g H}{3}}$

Step-by-step Solution

Detailed explanation

Given, P.E.=2K.E. now conservation of kinetic energy and potential energy, P.E.+K.E.=mgH⇒P.E.+12P.E.=mgH⇒32P.E.=mgH⇒P.E.=2mgH3=mgh⇒h=2H3 here the kinetic energy, 2K.E.+K.E.=mgH=3K.E.=312mv2v=2gH3

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A particle is released from a height H. At a certain height its kinetic energy is half of its potential energy with reference to the surface of the earth. Height and speed of the particle at that instant are respectively

Step-by-step Solution

A particle is released from a height $H$ . At a certain height its kinetic energy is half of its potential energy with reference to the surface of the earth. Height and speed of the particle at that instant are respectively