the depth d at which the value of acceleration due to

The depth $$d$$ at which the value of acceleration due to gravity becomes $$\frac{1}{n}$$ times the value at the surface of the earth, is
[$$R$$ = radius of the earth]

A. $$\frac{R}{n}$$

B. $$R\left( {\frac{{n - 1}}{n}} \right)$$

C. $$\frac{R}{{{n^2}}}$$

D. $$R\left( {\frac{n}{{n + 1}}} \right)$$

Answer : $$R\left( {\frac{{n - 1}}{n}} \right)$$

Solution :
$$\eqalign{ & g' = g\left( {1 - \frac{d}{R}} \right) \Rightarrow \frac{g}{n} = g\left( {1 - \frac{d}{R}} \right) \cr & \Rightarrow d = \left( {\frac{{n - 1}}{n}} \right)R \cr} $$

Releted MCQ Question on
Basic Physics >> Gravitation

Releted Question 1

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

A. Decrease

B. Remain unchanged

C. Increase

D. Be zero

View Answer

Releted Question 2

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

A. $$\frac{1}{2}\,mgR$$

B. $$2\,mgR$$

C. $$mgR$$

D. $$\frac{1}{4}mgR$$

View Answer

Releted Question 3

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A. $$64.5$$

B. $$129$$

C. $$182.5$$

D. $$730$$

View Answer

Releted Question 4

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

A. $$\frac{1}{2}\,hr$$

B. $$1 \,hr$$

C. $$2 \,hr$$

D. $$4 \,hr$$

View Answer

The depth $$d$$ at which the value of acceleration due to gravity becomes $$\frac{1}{n}$$ times the value at the surface of the earth, is
[$$R$$ = radius of the earth]

Releted MCQ Question on
Basic Physics >> Gravitation

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

Practice More Releted MCQ Question on
Gravitation

Practice More MCQ Question on Physics Section

The depth $$d$$ at which the value of acceleration due to gravity becomes $$\frac{1}{n}$$ times the value at the surface of the earth, is [$$R$$ = radius of the earth]

Releted MCQ Question on Basic Physics >> Gravitation

If the radius of the earth were to shrink by one percent, its mass remaining the same, the acceleration due to gravity on the earth’s surface would-

If $$g$$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth, is-

If the distance between the earth and the sun were half its present value, the number of days in a year would have been-

A geo-stationary satellite orbits around the earth in a circular orbit of radius $$36,000 \,km.$$ Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface $$\left( {{R_{earth}} = 6400\,km} \right)$$ will approximately be-

Practice More Releted MCQ Question on Gravitation

Practice More MCQ Question on Physics Section

The depth $$d$$ at which the value of acceleration due to gravity becomes $$\frac{1}{n}$$ times the value at the surface of the earth, is
[$$R$$ = radius of the earth]

Releted MCQ Question on
Basic Physics >> Gravitation

Practice More Releted MCQ Question on
Gravitation