Q126 / 150 · MHT CET 2024 (16 May Shift 2) · Physics

A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

  • Correct answer
    A
    32 N
  • B
    48 N
  • C
    96 N
  • D
    162 N

Solution

At height $\left(\mathrm{h}=\frac{\mathrm{R}}{\mathrm{n}}\right)$, the value of acceleration due to gravity is given by, $\mathrm{g}_{\mathrm{h}}=\left(\frac{\mathrm{n}}{\mathrm{n}+1}\right)^2 \mathrm{~g}$. For $\mathrm{n}=2$, $\begin{aligned} & \mathrm{g}_{\mathrm{h}}=\left(\frac{\mathrm{n}}{\mathrm{n}+1}\right)^2 \mathrm{~g}=\left(\frac{2}{2+1}\right)^2 \mathrm{~g}=\frac{4}{9} \mathrm{~g} \\ & \mathrm{~W}_{\mathrm{h}}=\mathrm{mg}_{\mathrm{h}}=\frac{4}{9} \times \mathrm{mg}=\frac{4}{9} \times 72=32 \mathrm{~N} \end{aligned}$

Hence, the correct answer is option: 'A'.

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