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The magnitude of the gravitational field...

The magnitude of the gravitational field at distance `r_(1)` and `r_(2)` from the centre of a uniform sphere of radius `R` and mass `M` are `F_(1)` and `F_(2)` respectively. Then:

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A, B
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The magnitude of gratitational field intensities at distance r_(1) and r_(2) from the centre of a uniform solid sphere of radius R and mass M are I_(1) and I_(2) respectively. Find the ratio of I_(1)//I_(2) if (a) r_(1) gt R and r_(2) gt R and (b) r_(1) lt R and r_(2) lt R (c ) r_(1) gt R and r_(2) lt R .

The magnitude of gravitational field at distances r_(1) and r_(2) from the centre of a uniform sphere of radius R and mass M , respectively. Find the ratio of (I_(1))//(I_(2))) if r_(1)gtR and r_(2)gtR .

Knowledge Check

  • The magnitudes of the gravitational field at distance r_(1) and r_(2) from the centre of a uniform sphere of radius R and mass M are E_(1) and E_(2) respectively. Then:

    A
    `(E_(1))/(E_(2))=(r_(1))/(r_(2))` if `r_(1)ltR` and `r_(2)ltR`
    B
    `(E_(1))/(E_(2))=(r_(2)^(2))/(r_(1)^(2))` if `r_(1)ltR` and `r_(2)ltR`
    C
    `(E_(1))/(E_(2))=(r_(2)^(2))/(r_(2)^(3))` if `r_(1)ltR` and `r_(2)ltR`
    D
    `(E_(1))/(E_(2))=(r_(1)^(2))/(r_(2)^(2))` if `r_(1)ltR` and `r_(2)ltR`

  • The magnitude of the gravitational field at distasnce r_(1) and r_(2) from the centre of a uniform sphere of radius R and mass M are E_(1) and E_(2) respectively. Then

    A
    `(E_(1))/(E_(2))=(r_(1))/(r_(2))` ir `r_(1)ltR` and `r_(2)ltR`
    B
    `(E_(1))/(E_(2))=(r_(2)^(2))/(r_(1)^(2))` if `r_(1)ltR` and `r_(2)ltR`
    C
    `(E_(1))/(E_(2))=(r_(1)^(3))/(r_(2)^(3))` if `r_(1)ltR` and `r_(2)ltR`
    D
    `(E_(1))/(E_(2))=(r_(1)^(2))/(r_(2)^(2))` ir `r_(1)ltR` and `r_(2)ltR`

  • The magnitudes of the gravitational field at distance r_(1)andr_(2) from the centre of a uniform sphere of radius R and mass M are F_(1)andF_(2) respectively. Then :

    A
    `(F_(1))/(F_(2))=(r_(1))/(r_(2))ifr_(1)ltR andr_(2)ltR`
    B
    `(F_(1))/(F_(2))=(r_(2)^(2))/(r_(1)^(2))ifr_(1)gtR andr_(2)gtR`
    C
    `(F_(1))/(F_(2))=(r_(1))/(r_(2))ifr_(1)gtR andr_(2)gtR`
    D
    `(F_(1))/(F_(2))=(r_(1)^(2))/(r_(2)^(2))ifr_(1)ltR andr_(2)ltR`

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