A body weighs 144 ,N at surface of earth. When it is taken to a height of h=3 ,R , where R is radius

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7.Gravitation

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A body weighs $144 \,N$ at the surface of earth. When it is taken to a height of $h=3 \,R$, where $R$ is radius of earth, it would weigh .......... $N$

$48$

$36$

$16$

$9$

Solution

(d)

Given that,

Weight of body $W =144\,N$

Height $h=3 R$

Radius of earth $= R$

We know that,

Acceleration due to gravity at the surface of the earth $= g$

Acceleration due to gravity at height $g ^{\prime}=3 R$

Now,

$\frac{ g }{ g ^{\prime}}=\left(\frac{ R }{ R + h }\right)^2$

$\frac{ g }{ g ^{\prime}}=\left(\frac{ R }{ R +3 R }\right)^2$

$\frac{ g }{ g ^{\prime}}=\frac{1}{16}$

Now, weight at the height

$\frac{ w ^{\prime}}{ w }=\frac{ mg }{ mg }$

$\frac{w^{\prime}}{w}=\frac{1}{16}$

$w^{\prime}=\frac{w}{16}$

$w^{\prime}=\frac{144}{16}$

$w^{\prime}=9\,N$

Hence, the weight at the height is $9\,N$

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A body weighs $144 \,N$ at the surface of earth. When it is taken to a height of $h=3 \,R$, where $R$ is radius of earth, it would weigh .......... $N$

Solution

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