1. The height of the point vertically above the earth’s surface, at which acceleration due to
gravity becomes 1% of its value at the surface is (Radius of the earth = R)

a) 8 R

b) 9 R

c) 10 R

d) 20 R

Explanation:

2. An object weights 72 N on earth. Its weight at a height of R/2 from earth is

a) 32 N

b) 56 N

c) 72 N

d) Zero

Explanation:

3. The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on 60^{o} latitude becomes zero is (Radius of earth =
6400 km. At the poles \[g=10ms^{-2 }\]

a) \[2.5\times10^{-3 }rad\diagup s\]

b) \[5.0\times10^{-1 }rad\diagup s\]

c) \[10\times10^{1 }rad\diagup s\]

d) \[7.8\times10^{-2 }rad\diagup s\]

Explanation:

4. Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine 100 km below the earth’s
surface (Given R = 6400 km)

a) 9.66 \[m\diagup s^{2 }\]

b) 7.64 \[m\diagup s^{2 }\]

c) 5.06 \[m\diagup s^{2 }\]

d) 3.10 \[m\diagup s^{2 }\]

Explanation:

5. If radius of earth is R then the height ‘h’ at which value of ‘g’ becomes one-fourth is

a) \[\frac{R}{4}\]

b) \[\frac{3R}{4}\]

c) R

d) \[\frac{R}{8}\]

Explanation:

6. R and r are the radii of the earth and moon
respectively. \[\rho_{e}\] and \[\rho_{m}\] are the densities of earth and moon respectively. The ratio of the accelerations due to gravity on the surfaces of earth and moon is

a) \[\frac{R}{r}\frac{\rho_{e}}{\rho_{m}}\]

b) \[\frac{r}{R}\frac{\rho_{e}}{\rho_{m}}\]

c) \[\frac{r}{R}\frac{\rho_{m}}{\rho_{e}}\]

d) \[\frac{R}{r}\frac{\rho_{m}}{\rho_{e}}\]

Explanation:

7. If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ‘g’ on earth is \[9.8 m\diagup s^{2 }\] , then the value of ‘g’ on that
planet is

a) 4.9 \[m\diagup s^{2 }\]

b) 0.98 \[m\diagup s^{2 }\]

c) 0.49 \[m\diagup s^{2 }\]

d) 49 \[m\diagup s^{2 }\]

Explanation:

8.Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If R_{e} is the maximum range of a projectile on the earth’s
surface, what is the maximum range on the surface of the moon for the same velocity of projection

a) \[0.2R_{e}\]

b) \[2 R_{e}\]

c) \[0.5 R_{e}\]

d) \[5 R_{e}\]

Explanation:

9. The angular speed of earth, so that the object on equator may appear weightless, is (g = 10 m/s^{2} , radius of earth 6400 km)

a) \[1.25\times 10^{-3}rad/sec\]

b) \[1.56\times 10^{-3}rad/sec\]

c) \[1.25\times 10^{-1}rad/sec\]

d) 1.56 \[rad/sec\]

Explanation:

10. At what distance from the centre of the earth, the value of acceleration due to gravity g will be half
that on the surface (R = radius of earth)

a) 2 R

b) R

c) 1.414 R

d) 0.414 R

Explanation: