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Gravitation question

2023 · 10 Apr · Shift 1 · Q63
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  5. /2023 · 10 Apr · Shift 1 · Q63

Gravitation question

2023 · 10 Apr · Shift 1 · Q63

JEE MainPhysicsGravitationMCQ+4 / −1
Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=R2d=\frac{R}{2}d=2R​ from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given R = radius of earth)
  1. A
    100 N
  2. B
    400 N
  3. C
    300 N
  4. D
    500 N
View written solutionFree

Correct answer: A

  1. Given:

    • Earth is assumed to be a sphere of uniform density.
    • Weight on the surface: W=200 NW = 200\,\text{N}W=200N
    • Depth from surface: d=R2d = \dfrac{R}{2}d=2R​

  2. **Formula for acceleration due to gravity at depth ddd: ** For a uniform spherical earth, gd=g(1−dR)g_d = g\left(1 - \frac{d}{R}\right)gd​=g(1−Rd​)

  3. Substitute d=R2d = \dfrac{R}{2}d=2R​: gd=g(1−R/2R)=g(1−12)=g2g_d = g\left(1 - \frac{R/2}{R}\right) = g\left(1 - \frac{1}{2}\right) = \frac{g}{2}gd​=g(1−RR/2​)=g(1−21​)=2g​

  4. **Weight is proportional to ggg: ** Wd=W⋅gdgW_d = W\cdot \frac{g_d}{g}Wd​=W⋅ggd​​ Wd=200×12=100 NW_d = 200 \times \frac{1}{2} = 100\,\text{N}Wd​=200×21​=100N

  5. Check options:

    • A: 100 N100\,\text{N}100N ✅
    • B: 400 N400\,\text{N}400N ❌
    • C: 300 N300\,\text{N}300N ❌
    • D: 500 N500\,\text{N}500N ❌

Therefore, the correct answer is A.

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