JEE MainPhysicsGravitation
A body of mass m is moved from the centre of the Earth to a distance r = 2R from the centre, where R is the radius of the Earth. Assuming the Earth to be a uniform solid sphere, which of the following correctly describes the variation of the weight W of the body with the radial distance r ?
Options
- AW decreases as 1 r^2 for all r > 0 .
- BW increases linearly with r for r R .
- CW is constant for r R .
- DW increases as r^2 for r R .
Correct answer
B. W increases linearly with r for r R .
Step-by-step solution
Inside the Earth ( r Since the weight is W = mg(r) , we have W r . Thus, the weight increases linearly with r for r Outside the Earth ( r > R ), the acceleration due to gravity is g(r) = GM r^2 . Therefore, the weight is W = GMm r^2 , which means W 1 r^2 . Thus, the weight decreases as 1 r^2 for r > R . This matches the description where W increases linearly for r R . Answer: W increases linearly with r for r R .