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A planet of radius R=(1)/(10)xx(radius o...

A planet of radius `R=(1)/(10)xx(radius of Earth)` has the same mass density as Earth. Scientists dig a well of depth`(R )/(5)` on it and lower a wire of the same length and a linear mass density `10^(-3) kg m(_1)` into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it inplace is (take the radius of Earth`=6xx10^6m` and the acceleration due to gravity on Earth is `10ms^(-2)`

A

96 N

B

108 N

C

120 N

D

150 N

Text Solution

Verified by Experts

The correct Answer is:
B
`E_(G)=(4piGrrho)/(3)`
`dF=E_(G)lamdadr`
`F=underset((4R)/(5))overset(R)int(4piGrholamda)/(3)rdr=(4piGrholamda)/(3)[(r^(2))/(2)]_((4R)/(5))^(R)`
`=(4piGrholamda)/(3xx2)[R^(2)-(16R^(2))/(25)]=(4pi)/(6)Grholamdaxx(9)/(25)R^(2)`
`F=(4pi)/(6)Gxx(M)/((4pi)/(3)R_(e)^(3))xxlamdaxx(9)/(25)xx(R_(e)^(2))/(100)`
After solving [`Fimplies108N]`
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