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Gravitation question

2023 · 8 Apr · Shift 1 · Q63
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  5. /2023 · 8 Apr · Shift 1 · Q63

Gravitation question

2023 · 8 Apr · Shift 1 · Q63

JEE MainPhysicsGravitationMCQ+4 / −1
The weight of a body on the earth is 400 N400 \mathrm{~N}400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:
  1. A
    300 N
  2. B
    200 N
  3. C
    100 N
  4. D
    Zero
View written solutionFree

Correct answer: B

  1. Given:

    • Weight on the surface of Earth: W=400 NW = 400\,\text{N}W=400N
    • Depth below surface: d=R2d = \dfrac{R}{2}d=2R​, where RRR is the radius of Earth

  2. **Formula for acceleration due to gravity at depth ddd: ** Inside the Earth, gravity decreases linearly with depth: 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(1−12)=g2g_d = g\left(1 - \frac{1}{2}\right) = \frac{g}{2}gd​=g(1−21​)=2g​

  4. Weight at depth: Since weight is proportional to ggg, Wd=W⋅gdg=400⋅12=200 NW_d = W\cdot \frac{g_d}{g} = 400 \cdot \frac{1}{2} = 200\,\text{N}Wd​=W⋅ggd​​=400⋅21​=200N

  5. Check options:

    • A: 300 N300\,\text{N}300N →\rightarrow→ incorrect
    • B: 200 N200\,\text{N}200N →\rightarrow→ correct
    • C: 100 N100\,\text{N}100N →\rightarrow→ incorrect
    • D: Zero →\rightarrow→ incorrect

Final Answer: 200 N200\,\text{N}200N

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