Question

NTSE physics question Two bodies of equal weight are kept at height of h and 1.5h respectively. The ratio of their Potential Energy is 1. 3:2 2. 2:3 3. 1:1 4. None of these Please explain! Thanks

Answer 1

Two bodies of equal weight are kept at height of h and 1.5h respectively. The ratio of their Potential Energy is 2:3 

Answer 2

Answer:  

The ratio of potential energies $\bold{\mathrm{P}_{\mathrm{A}} : \mathrm{P}_{\mathrm{B}} \text { is } 2 : 3.}$

Solution:

The potential energy is the energy possessed by the body at rest. The mathematical representation of potential energy is  

Potential Energy = mgh

Here, m is the ‘mass of the body’, g is the ‘acceleration due to gravity’ acting on the body and h is the ‘height of the body’ placed above from ground

Let $P_{A} \text { and } P_{B}$ be the potential energies for the two bodies A and B. As the both bodies have equal weight, that means mg is equal for both the bodies.

Let us consider $\mathrm{h}_{\mathrm{A}} \text { and } \mathrm{hB}$ are the heights at which both the bodies are kept.

So, it is known that, $\mathrm{h}_{\mathrm{A}}=\mathrm{h} \text { and } \mathrm{h}_{\mathrm{B}}=1.5 \mathrm{h}$

The potential energies for both the bodies are

${P_{A}=m g h_{A}=m g h} \\ \\ {P_{B}=m g h_{B}=1.5 m g h}\end{array}$

So the ratio of their potential energies are

$\frac{P_{A}}{P_{B}}=\frac{m g h}{1.5 m g h}=\frac{1}{1.5}$

If we multiply the numerator and denominator by 10, we will get

$\frac{P_{A}}{P_{B}}=\frac{10}{15}=\frac{2}{3}$

Thus the ratio of potential energies $\bold{\mathrm{P}_{\mathrm{A}} : \mathrm{P}_{\mathrm{B}} \text { is } 2 : 3.}$