Variation of g with altitude, depth and rotation — practice questions

Question 1 · difficulty L2 · understanding

The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $\frac{g}{9}$, where $g$ is acceleration due to gravity on earth's surface, is $\_\_\_\_$ .

• A. $\sqrt{3} R$
• B. $2 \sqrt{2} R$
• C. $2 R$
• D. ${\frac{4}{9} R}$

Question 2 · difficulty L2 · understanding

Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \mathrm{~N}$$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

• A. 75 N
• B. 375 N
• C. 300 N
• D. 225 N

Question 3 · difficulty L2 · understanding

A $$90 \mathrm{~kg}$$ body placed at $$2 \mathrm{R}$$ distance from surface of earth experiences gravitational pull of : ($$\mathrm{R}=$$ Radius of earth, $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$)

• A. 300 N
• B. 225 N
• C. 100 N
• D. 120 N

Question 4 · difficulty L2 · understanding

The acceleration due to gravity on the surface of earth is $$\mathrm{g}$$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

• A. g/4
• B. 2g
• C. g/2
• D. 4g

Question 5 · difficulty L2 · understanding

Two planets A and B of radii $$\mathrm{R}$$ and 1.5 R have densities $$\rho$$ and $$\rho / 2$$ respectively. The ratio of acceleration due to gravity at the surface of $$\mathrm{B}$$ to $$\mathrm{A}$$ is:

• A. 2 : 1
• B. 2 : 3
• C. 4 : 3
• D. 3 : 4

Question 6 · difficulty L2 · understanding

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $$\rho$$ and $$\rho / 3$$ respectively. The ratio of acceleration due to gravity at their surfaces $$\left(g_{A}: g_{B}\right)$$ will be:

• A. 3 : 16
• B. 4 : 3
• C. 1 : 16
• D. 3 : 4

Question 7 · difficulty L2 · understanding

Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below

• A. Statement I is false but statement II is true
• B. Statement I is true but statement II is false
• C. Both Statement I and Statement II are true
• D. Both Statement I and Statement II are false

Question 8 · difficulty L2 · understanding

The acceleration due to gravity at height $$h$$ above the earth if $$h << \mathrm{R}$$ (Radius of earth) is given by

• A. $$g^{\prime}=g\left(1-\frac{2 h}{R}\right)$$
• B. $$g^{\prime}=g\left(1-\frac{2 h^{2}}{R^{2}}\right)$$
• C. $$g^{\prime}=g\left(1-\frac{h^{2}}{2 R^{2}}\right)$$
• D. $$g^{\prime}=g\left(1-\frac{h}{2 R}\right)$$

Question 9 · difficulty L2 · understanding

The weight of a body on the earth is $$400 \mathrm{~N}$$. Then weight of the body when taken to a depth half of the radius of the earth will be:

• A. 300 N
• B. 200 N
• C. 100 N
• D. Zero

Question 10 · difficulty L2 · understanding

The weight of a body on the surface of the earth is $$100 \mathrm{~N}$$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

• A. 50 N
• B. 64 N
• C. 25 N
• D. 100 N