Gravitation Worksheet-2

Gravitation Worksheet-2

 

  1. Calculate the force of gravitation due to earth on a ball of 1 kg mass lying on the ground. (Mass of earth = 6 × 1024 kg; Radius of earth = 6.4 × 103 km; and G = 6.7 × 10–11 Nm2/Kg2)

A. 9.8 newtons                              B. 10 newtons

C. 9.8 kg                                         D. 9.8 newton meter

 

  1. The mass of the earth is 6.4 × 1024 kg and that of the moon is 7.4 × 1022 kg. if the distance between the earth and the moon be 3.84 × 105 km, calculate the force exerted by the earth on the moon.  (G = 6.7 × 10–11 Nm2 kg–2)

A. F = 2.01 × 1010 newtons

B. F = 2.01 × 1020 kg

C. F = 2.01 × 1920 newton meter

D. F = 2.01 × 1020 newtons

 

  1. Calculate the value of acceleration due to gravity on the surface of the moon. (Given Mass of the moon = 7.4 × 1022 kg; Radius of moon = 1740 km; G = 6.67 × 10–11 Nm2 /kg2)

A. –1.63 m/s2   B. 1.63 m/s        C. 1.63 m/s2      D. 9.8 m/s2

 

  1. The earth’s gravitational force causes an acceleration of 5 m/s2 in a 1 kg mass somewhere in space. How much will the acceleration of a 3 kg mass be at the same place ?

A. 5 m/s2           B. -5 m/s2          C. 15 m/s2          D. 5/3 m/s2

 

  1. To estimate the height of a bridge over a river, a stone is dropped freely in the river from the bridge. The stone takes 2 seconds to touch the water surface in the river. Calculate the height of the bridge from the water level (g = 9.8 m/s2)

A. 39.2 m           B. 20 m              C. 9.8 m             D. 19.6 m

 

Answer Key:

  1. A

Explanation: The force of gravitation is calculation is calculated by using the formula:

         

Gravitational constant, G = 6.7 × 10–11 Nm2/Kg2

Mass of earth, m1 = 6 × 1024 kg            

Mass of ball, m2 = 1 kg

Distance between centre of earth and ball

          r = Radius of earth

          = 6.4 × 103 km

          = 6.4 × 103 × 1000m

          = 6.4 × 106 km

By putting these values in the formula, we get :

Or     F = 9.8 newtons

Thus, the earth exerts a gravitational force of 9.8 newtons on a ball of mass 1 kilogram. This is a comparatively large force. It is due to this large gravitational force exerted by earth that when the 1 kg ball is dropped from a height, it falls to the earth.

 

  1. D

Explanation: The force exerted by one body on another body is given by the newton’s formula:

         

Here, Gravitational constant, G = 6.7 × 10–11 Nm2 kg–2

          Mass of the earth, m1 = 6 × 1024 kg

          Mass of the moon, m2 = 7.4 × 1022 kg

          Distance between Earth and moon

r = 3.84 × 105 km

= 3.84 × 108 km

By putting the values in the  formula, we get :

F = 2.01 × 1020 newtons

Thus, the gravitational force exerted by the earth on the moon is 2.01 × 1020 newtons. And this is an extremely large force. It is this extremely large gravitational force exerted by the earth on the moon which makes the moon revolve around the earth.

 

  1. C

Explanation: The formula for calculating the acceleration due to gravity is :

         

Gravitational constant, G = 6.7 × 10–11 Nm2/kg2

Mass of the moon, M = 7.4 × 1022 kg

Radius of the moon, R = 1740 km

          1.74 × 106 m

Now, putting these values in the formula, we get :

Or     g = 1.63 m/s2

Thus, the acceleration due to gravity, g, on the surface of the moon is 1.63 m/s2.

 

  1. A

Explanation: The acceleration produced by the gravitational force of earth does not depend on the mass of the object. So, the acceleration produced in the 3 kg mass will be the same as that produced in 1 kg mass. That is, the acceleration produced will be 5 m/s2.

 

  1. D

Explanation: The stone is dropped freely from rest, so the initial velocity of the stone, u = 0. Again, the velocity of stone is increasing as it comes down, so the acceleration due to gravity, g, is positive.

Now, initial velocity of stone, u = 0

Time taken, t = 2 s

Acceleration due to gravity, g = 9.8 m/s2 (stone is coming down)

And, Height of the bridge, h = ?

For a freely falling body :

Height, h = ut + (1/2) gt2

Putting the values in the formula, we get :

         

Or    

Or     h = 19.6 m

Thus, the height of bridge above the water level is 19.6 metres.