Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed 250 N on the surface?

Asked by Pragya Singh | 1 year ago |  68

##### Solution :-

Weight of a body on the Earth’s surface, W=mg=250 N

Radius of the Earth = Re

Let d be at a distance halfway to the centre of the earth,

$$d= \dfrac{R_e}{2}$$

Acceleration due to gravity at d is given by the relation

gd=$$( \dfrac{(1− d}{R_e})g$$

gd=$$(\dfrac{1−R_e}{2R_e})g$$

=$$\dfrac{g}{2}$$

Weight of the body at depth d,

W′=mgd

=$$\dfrac{mg}{2}$$$$\dfrac{W}{2}$$$$\dfrac{250}{2}$$

=125 N

Answered by Abhisek | 1 year ago

### Related Questions

#### A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1.

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4×1023 kg; radius of mars = 3395 km; G = 6.67×10-11 N m2 kg–2.

#### A spaceship is stationed on Mars. How much energy must be expended on the spaceship

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the sun = 2×1030 kg; mass of mars = 6.4×1023 kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 ×108 km; G = 6.67×10-11 N m2kg–2.

#### A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (mass of the sun = 2×1030 kg).