Understanding of Field

Q.

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively ${\rho }_{1}and{\rho }_2$. The ratio of the accelerations due to gravity at their surface is

1. $g_1:g_2=\frac{{\rho }_1}{R_1^2}:\frac{{\rho }_1}{R_2^2}$

2. $g_1:g_2=R_1{R}_2:{\rho }_1{\rho }_2$

3. $g_1:g_2=R_1{\rho }_2:R_2{\rho }_1$

4. $g_1:g_2=R_1{\rho }_1:R_2{\rho }_2$

Q.

The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

1. $\frac{g}{9}$

2. $\frac{g}{3}$

3. $\frac{g}{4}$

4. $g$

Q. There exists a spherically symmetric gravitational system of particles of radius $R$. Its speed $V$ as a function of distance $r(0<r<\infty )$ from the centre of the system is represented by

1. 
2. 
3. 
4. 

Q.

A point $\rho$ lies on the axis of a ring of mass M and radius $\alpha$, at a distance $\alpha$, from its centre C, A small particle starts from $\rho$ and reaches C under gravitational attraction only.Its speed at C will be

1. $\sqrt{\frac{2GM}{\alpha }}$

2. $\sqrt{\frac{2GM}{\alpha }}(1-\frac{1}{\sqrt{2}})$

3. $\sqrt{\frac{2GM}{\alpha }}(\sqrt{2}-1)$

4. Zero

Q. A weight is suspended from the ceiling of a lift by a spring balance. When the lift is stationary the spring balance reads W. If the lift suddenly falls freely under gravity, the reading on the spring balance will be

1. W
2. 2 W
3. $\frac{W}{2}$
4. \N

Q. The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

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