Question

Two bodies of equal masses are placed at heights h and 2h, find ratio of their g.p.e
(gravitational potential energies)?
(Do your best, need good answers;))

Answer 1

EXPLANATION :-

GIVEN :-

• Two bodies of equal masses are placed at heights h and 2h.

TO FIND :-

• Ratio of their gravitational potential energies.

SOLUTION :-

We have :

⇒ Height (H₁) = h

⇒ Height (H₂) = 2h

⇒ Mass (M₁) = m

⇒ Mass (M₂) = m

Gravitational potential energies :

⇒ G.P.E [1] = mgH₁ = mgh

⇒ G.P.E [2] = mgH₂ = mg(2h)

Ratio of their G.P.E's :

⇒ mgh/mg(2h)

⇒ mgh/2mgh

⇒ 1/2

∴ The ratio of their gravitational potential energies is 1 : 2.

Answer 2

$\large \rm {\underbrace{\underline{Elucidation:-}}}$

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$\sf \red {\underline{\underline{Provided\: that:-}}}$

$\to \tt {Mass(m)\: of\: two\: bodies\: are\: equal}$

$\to \tt {Height\: of\: first\: body\: is\: h}$

$\to \tt {Height\: of\: second\: body\: is\: 2h}$

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$\sf \blue {\underline{\underline{To\: determine:-}}}$

$\to \tt {Ratio\: of\: their\: gravitational\: potential\: energies=?}$

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$\sf \pink{\underline{\underline{We\: Know:-}}}$

$\implies \tt {\boxed{\underline{Gravitational\: potential\: energy(G.P.E)=mgh}}}$

➻So, according to the formula,

$\to \tt {G.P.E\: of\: first\: body=m×g×h}$

$\to \tt {G.P.E\: of\: second\: body=m×g×2h}$

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➻To obtain the ratio,

$\to \tt {G.P.E\: of\: first\: body\: : \:G.P.E\: of\: second\: body}$

$\to \tt { m×g×h\: : \:m×g×2h}$

$\to \tt \green {\fbox{\underline{ 1:2}}}$

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$\sf \purple {\underline{\underline{Therefore,}}}$

➻Ratio of their gravitational potential energies is 1:2

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