Assuming the earth to be a sphere of uniform | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) At the surface of the earth, the weight of the body is given by $W_s = mg_s = 300 \,N$.The acceleration due to gravity at a depth $d$ below the su

Vedclass · Accepted Answer

$225$

Vedclass · Answer

(D) At the surface of the earth, the weight of the body is given by $W_s = mg_s = 300 \,N$.The acceleration due to gravity at a depth $d$ below the surface of the earth is given by the formula $g_d = g_s \left(1 - \frac{d}{R}ight)$, where $g_s$ is the acceleration due to gravity at the surface and $R$ is the radius of the earth.Given the depth $d = R/4$, we substitute this into the formula:$g_d = g_s \left(1 - \frac{R/4}{R}ight)$$g_d = g_s \left(1 - \frac{1}{4}ight)$$g_d = g_s \left(\frac{3}{4}ight)$The weight of the body at depth $d$ is $W_d = mg_d$.Substituting $g_d$ into the weight equation:$W_d = m 	imes \left(\frac{3}{4} g_sight)$$W_d = \frac{3}{4} 	imes (mg_s)$Since $mg_s = 300 \,N$, we have:$W_d = \frac{3}{4} 	imes 300 \,N = 225 \,N$.

Assuming the earth to be a sphere of uniform mass density, a body weighs $300 \,N$ on the surface of the earth. How much would it weigh at a depth of $R/4$ below the surface of the earth (in $\,N$)?

Similar Questions

Assuming the Earth to be a sphere of uniform density, the acceleration due to gravity:

The masses of two planets are in the ratio $1 : 2$. Their radii are in the ratio $1 : 2$. The ratio of the acceleration due to gravity on the planets is:

The figure shows the variation of acceleration due to gravity with distance from the center of a uniform spherical planet of radius $R$. What is $r_2 - r_1$?

At what height from the surface of the earth will the value of acceleration due to gravity fall to half of its value on the surface of the earth?

Acceleration due to gravity is $g$ on the surface of the earth. The value of acceleration due to gravity at a height of $32 \, km$ above the earth's surface is ........ $g$. (Radius of the earth $= 6400 \, km$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module