The weight of a body of mass m decreases by 1 | vedclass

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

Question

(B) The change in acceleration due to gravity at height $h$ is given by $\frac{\Delta g_h}{g} \approx \frac{2h}{R}$.Given that the weight decreases by

Vedclass · Accepted Answer

$0.5\%$ decrease

Vedclass · Answer

(B) The change in acceleration due to gravity at height $h$ is given by $\frac{\Delta g_h}{g} \approx \frac{2h}{R}$.Given that the weight decreases by $1\%$,we have $\frac{2h}{R} 	imes 100\% = 1\%$,which implies $\frac{h}{R} = 0.005$.At a depth $d = h$,the change in acceleration due to gravity is given by $\frac{\Delta g_d}{g} = \frac{d}{R} = \frac{h}{R}$.Substituting the value of $\frac{h}{R}$,we get $\frac{\Delta g_d}{g} = 0.005$.Therefore,the percentage decrease in weight at depth $h$ is $0.005 	imes 100\% = 0.5\%$.

The weight of a body of mass $m$ decreases by $1\%$ when it is taken to a height $h$ above the surface of the Earth. What is the percentage decrease in its weight when it is taken to a depth $h$ below the surface of the Earth?

Similar Questions

Let $g$ be the acceleration due to gravity at the Earth's surface and $K$ be the rotational kinetic energy of the Earth. Suppose the Earth's radius decreases by $2 \%$ keeping its mass the same,then:

$A$ body weighs $500 \,N$ on the surface of the earth. At what distance below the surface of the earth will it weigh $250 \,N$ (in $\,km$)? (Radius of earth, $R = 6400 \,km$)

When one moves from a point $16 \text{ km}$ below the earth's surface to a point $16 \text{ km}$ above the earth's surface, the change in $g$ is approximately $\alpha \%$. The value of $\alpha$ is . . . . . . . (Take radius of the earth $R = 6400 \text{ km}$.)

$A$ simple pendulum has a time period $T_1$ when on the earth's surface and $T_2$ when taken to a height $R$ above the earth's surface,where $R$ is the radius of the earth. The value of $T_2/T_1$ is

The average density of the Earth is [ $g$ is acceleration due to gravity]:

Vedclass Test Series

Exam Paper Generator

Online Exam Module