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Gravitation question

2021 · 27 Aug · Shift 2 · Q49
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  5. /2021 · 27 Aug · Shift 2 · Q49

Gravitation question

2021 · 27 Aug · Shift 2 · Q49

JEE MainPhysicsGravitationMCQ+4 / −1
A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :
  1. A
    −-− 60 G
  2. B
    +2 G
  3. C
    −-− 20 G
  4. D
    −-− 4 G
View written solutionFree

Correct answer: D

  1. Given data

    • Mass at centre: m1=50 kgm_1 = 50\,\text{kg}m1​=50kg
    • Mass of spherical shell: m2=100 kgm_2 = 100\,\text{kg}m2​=100kg
    • Radius of shell: R=50 mR = 50\,\text{m}R=50m
    • Point is at distance: r=25 mr = 25\,\text{m}r=25m from centre

  2. Gravitational potential due to the point mass at the centre The potential at distance rrr from a point mass is V1=−Gm1rV_1 = -\frac{Gm_1}{r}V1​=−rGm1​​ So, V1=−G⋅5025=−2GV_1 = -\frac{G\cdot 50}{25} = -2GV1​=−25G⋅50​=−2G

  3. Gravitational potential due to the spherical shell For a uniform spherical shell, the gravitational potential at any point inside the shell is constant and equal to the potential at the surface: V2=−Gm2RV_2 = -\frac{Gm_2}{R}V2​=−RGm2​​ Therefore, V2=−G⋅10050=−2GV_2 = -\frac{G\cdot 100}{50} = -2GV2​=−50G⋅100​=−2G

  4. Total gravitational potential Potentials add algebraically: V=V1+V2=−2G+(−2G)=−4GV = V_1 + V_2 = -2G + (-2G) = -4GV=V1​+V2​=−2G+(−2G)=−4G

  5. Matching with options The value of VVV is −4G\boxed{-4G}−4G​ So the correct option is D.

  6. Comparison with stored answer Stored correct answer: D

    This matches our derived answer.

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