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7.Gravitation
medium
The weight of a body on the earth is $400\,N$. Then weight of the body when taken to a depth half of the radius of the earth will be ............ $N$
A$0$
B$300$ $N$
C$100$ $N$
D$200$ $N$
(JEE MAIN-2023)
Solution
$W = mg =400\,N$
At depth $d$, gravity $g ^{\prime}= g \left(1-\frac{ d }{ R }\right)$
For $d=\frac{R}{2} \quad g^{\prime}=g\left(1-\frac{R}{2 R}\right)=\frac{g}{2}$
$W ^{\prime}= m g ^{\prime}=\frac{ mg }{2}=200\,N$
At depth $d$, gravity $g ^{\prime}= g \left(1-\frac{ d }{ R }\right)$
For $d=\frac{R}{2} \quad g^{\prime}=g\left(1-\frac{R}{2 R}\right)=\frac{g}{2}$
$W ^{\prime}= m g ^{\prime}=\frac{ mg }{2}=200\,N$
Standard 11
Physics
