What should be the velocity of earth due to rotation about its own axis so that the weight at equator become 3/5 of initial value. Radius of earth on equator is 6400 km

1.  $7.4\times {10}^{-4}$ rad/sac             

2.  6.4$\times {10}^{-4}$ rad/sac

3.  $7.8\times {10}^{-4}$ rad/sac               

4.  8.7$\times {10}^{-4}$ rad/sac 

Acceleration due to gravity is ‘g’ on the surface of the earth. The value of acceleration due to gravity at a height of 32 km above earth’s surface is (Radius of the earth = 6400 km)

1. 0.9 g           

2. 0.99 g

3. 0.8 g           

4. 1.01 g

The height of a point vertically above the earth’s surface, at which the acceleration due to gravity becomes \(1\%\) of its value at the surface is: (Radius of the earth = \(R\))
1. \(8R\)
2. \(9R\)
3. \(10R\)
4. \(20R\)

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

1. $\frac{R}{4}$               

2. $\frac{3R}{4}$

3. R                 

4. $\frac{R}{8}$

Two planets have the same average density but their radii are $R_1$  and $R_2$. If acceleration due to gravity on these planets be $g_1$ and $g_2$ respectively, then

1.  $\frac{g_1}{g_2}$= $\frac{R_1}{R_2}$                   

2. $\frac{g_1}{g_2}$=$\frac{R_2}{R_1}$

3.  $\frac{g_1}{g_2}$= $\frac{{R_1}^2}{{R_2}^2}$                  

4. $\frac{g_1}{g_2}$= $\frac{{R_1}^3}{{R_2}^3}$

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 ?

1. 0.2$R_{\epsilon }$                     

2. 2$R_{\epsilon }$

3. 0.5$R_{\epsilon }$                     

4. 5$R_{\epsilon }$

If the density of the earth is increased \(4\) times and its radius becomes half of what it is, our weight will be:
1. four times the present value
2. doubled
3. the same
4. Halved

When a body is taken from the equator to the poles, its weight 
1.   Remains constant           

2.  Increases

3.  Decreases                    

4.  Increases at N-pole and decreases at S-pole

A body weighs 700 gm wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass $\frac{1}{7}$ of earth's mass and radius is half that of the earth ?

1.  200 gm wt                         

2.  400 gm wt     

3.  50 gm wt

4.  300 gm wt