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# Given the formula T , If t is doubled and r is doubled and r is

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Senior Manager
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Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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18 Apr 2019, 15:18
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35% (medium)

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69% (01:33) correct 31% (02:51) wrong based on 16 sessions

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Given the formula T = $$2\pi$$$$\sqrt{\frac{r^3}{GX}}$$, If T is doubled and r is doubled, by what factor does X change?

A)$$\frac{1}{4}$$
B)$$\frac{1}{2}$$
C)1
D)2
E)4

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Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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Updated on: 19 Apr 2019, 04:54
we have to make LHS = RHS
if T and r are doubled, $$(2T)^1$$ become $$2T$$, while $$(2r)^\frac{3}{2}$$ become $$2\sqrt{2}*r^\frac{3}{2}$$ :

2*T = $$2\pi$$$$\sqrt{\frac{r^3}{GX}}$$*$$2\sqrt{2}$$
T = $$2\pi$$$$\sqrt{\frac{r^3}{GX}}$$*$$\sqrt{2}$$

so to equalize the $$\sqrt{2}$$ in the RHS,
the RHS should be divided by $$\sqrt{2}$$
so $$\sqrt{X}$$ become $$\sqrt{2X}$$, or X become 2X ---> D
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Originally posted by Mahmoudfawzy83 on 19 Apr 2019, 00:05.
Last edited by Mahmoudfawzy83 on 19 Apr 2019, 04:54, edited 1 time in total.
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Re: Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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19 Apr 2019, 03:57
Mahmoudfawzy83 wrote:
we have to make LHS = RHS
if T and r are doubled, $$(2T)^1$$ become $$2T$$, while $$(2r)^\frac{3}{2}$$ become $$2\sqrt{2}*r^\frac{3}{2}$$ :

2*T = $$2\pi$$$$\sqrt{\frac{r^3}{GX}}$$*$$2\sqrt{2}$$
T = $$2\pi$$$$\sqrt{\frac{r^3}{GX}}$$*$$\sqrt{2}$$

so to equalize the $$\sqrt{2}$$ in the RHS,
the RHS should be divided by $$\sqrt{2}$$
or $$\sqrt{X}$$ = $$\sqrt{2}$$, so X = 2 ---> D

can you make this more clear.. i couldnt understand it !
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Given the formula T , If t is doubled and r is doubled and r is  [#permalink]

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19 Apr 2019, 07:56
Hi, payalpathak
I will explain it step-wise

First, we can simplify the equality to:
T = k*$$\sqrt{\frac{r^3}{X}}$$

Second, separate the variable we want to examine in the LHS, while other variables in the RHS.
$$X = k^2*\frac{r^3}{T^2}$$

third, apply the changes (T become 2T, and r become 2r) to see how X will change:
$$k^2*\frac{(2r)^3}{(2T)^2}$$ = $$k^2*\frac{8r^3}{4T^2}$$ = $$2*(k^2*\frac{r^3}{T^2})$$ $$= 2X$$

so when T and r are doubled, X will become 2X (doubled also)
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Given the formula T , If t is doubled and r is doubled and r is   [#permalink] 19 Apr 2019, 07:56
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