Back to Directory
NEET PHYSICSEasy

A body weighs 200 N200 \text{ N} on the surface of the earth. How much will it weigh halfway down the centre of the earth?

A

100 N100 \text{ N}

B

150 N150 \text{ N}

C

200 N200 \text{ N}

D

250 N250 \text{ N}

Step-by-Step Solution

  1. Formula for Gravity at Depth: The acceleration due to gravity (gdg_d) at a depth dd below the surface of the Earth is given by the formula: gd=g(1−dRE)g_d = g \left( 1 - \frac{d}{R_E} \right) where gg is the acceleration due to gravity on the surface and RER_E is the radius of the Earth [Eq. 7.19].
  2. Given Data:
  • Weight on surface, W=mg=200 NW = mg = 200 \text{ N}.
  • Depth, d=RE2d = \frac{R_E}{2} (halfway to the centre).
  1. Calculation: The new weight WdW_d is mgdm g_d. Wd=mg(1−RE/2RE)W_d = m g \left( 1 - \frac{R_E/2}{R_E} \right) Wd=W(1−12)W_d = W \left( 1 - \frac{1}{2} \right) Wd=200(0.5)=100 NW_d = 200 \left( 0.5 \right) = 100 \text{ N}
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started