Graph of Variation of G

Q.

If the radius of earth shrinks by 1.5 percent (mass remaining same), then the value of gravitational acceleration changes by

1. $2\%$

2. $-2\%$

3. $3\%$

4. $-3\%$

Q.

A planet has mass $\frac{1}{10}$ of that of earth, while radius is $\frac{1}{3}$ that of earth. If a person can throw a stone on earth surface to a height of 90m, then he will be able to throw the stone on that planet to a height

1. 90 m

2. 40 m

3. 100 m

4. 45 m

Q.

Derive the relation between g and G. $\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$

Q. Which one of the following graphs represents correctly the variation of the gravitational field (I) with the distance (r) from the centre of a spherical shell of mass M and radius a

1. 
2. 
3. 
4. 

Q.

Acceleration due to gravity on moon is $\frac{1}{6}$ of the acceleration due to gravity on earth. If the ratio of densities of earth $\left({\rho }_m\right)$ and moon $\left({\rho }_e\right)$ is $\left(\frac{{\rho }_e}{{\rho }_m}\right)=\frac{5}{3}$ then radius of moon $R_m$ in terms of $R_e$ will be

1. $\frac{5}{18}{R}_e$

2. $\frac{1}{6}{R}_e$

3. $\frac{3}{18}{R}_e$

4. $\frac{1}{2\sqrt{3}}{R}_e$

Q. Which one of the following graphs represents correctly the variation of the gravitational field (I) with the distance (r) from the centre of a spherical shell of mass M and radius a

1. 
2. 
3. 
4. 

Q. Consider the earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The gravitational field measured by

1. A goes on decreasing and that by $B$ goes on increasing.
2. Each remains unchanged
3. $B$ goes on decreasing and that by $A$ goes on increasing.
4. Each goes on decreasing.

Q. In the following four periods
(i) Time of revolution of a satellite just above the earth’s surface $\left(T_{st}\right)$
(ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth $\left(T_{ma}\right)$
(iii) Period of simple pendulum having a length equal to the earth’s radius in a uniform field of 9.8 N/k $\left(T_{sp}\right)$
(iv) Period of an infinite length simple pendulum in the earth’s real gravitational field $\left(T_{is}\right)$

1. $T_{st}>T_{ma}$
2. $T_{ma}>T_{st}$
3. $T_{sp}<T_{is}$
4. $T_{st}=T_{ma}=T_{sp}=T_{is}$