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

 (a)  $7.4\times {10}^{-4}$ rad/sac             

 (b)  6.4$\times {10}^{-4}$ rad/sac

 (c)  $7.8\times {10}^{-4}$ rad/sac               

(d)  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) 0.99g

(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 ?

(a) 0.2$R_{\epsilon }$                     

(b) 2$R_{\epsilon }$

(c) 0.5$R_{\epsilon }$                     

(d) 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 of mass m is taken to the bottom of a deep mine. Then 

(1)   Its mass increases 

(2)  Its mass decreases

(3)   Its weight increases

(4)  Its weight decreases

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