Assuming earth to be a sphere of uniform mass density, weight of a body at a depth d=frac{R}{2} from

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7.Gravitation

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Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d=\frac{R}{2}$ from the surface of earth, if its werght on the surface of earth is $200\,N$, will be $...........\,N$ ( $Given R =$ Radrus of earth)

A

$400$

B

$500$

C

$300$

D

$100$

(JEE MAIN-2023)

Solution

$M =\frac{ W }{ g }=\frac{200}{10}=20\,kg$

Acc. due to gravity at a depth $g^{\prime}= g \left(1-\frac{ d }{ R }\right)$

$d \rightarrow$ depth from surface

$d =\frac{ R }{2}$

$g ^{\prime}= g \left(1-\frac{ R / 2}{ R }\right)=\frac{ g }{2}=5 m / s ^2$

weight $= m \times g$

at depth $R / 2=20 \times 5=100\,N$

Standard 11

Physics

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