Gravitation Worksheet-2
A. 9.8 newtons B. 10 newtons
C. 9.8 kg D. 9.8 newton meter
A. F = 2.01 × 10^{10} newtons
B. F = 2.01 × 10^{20} kg
C. F = 2.01 × 19^{20} newton meter
D. F = 2.01 × 10^{20} newtons
A. –1.63 m/s^{2} B. 1.63 m/s C. 1.63 m/s^{2} D. 9.8 m/s^{2}
A. 5 m/s^{2} B. -5 m/s^{2} C. 15 m/s^{2} D. 5/3 m/s^{2}
A. 39.2 m B. 20 m C. 9.8 m D. 19.6 m
Answer Key:
Explanation: The force of gravitation is calculation is calculated by using the formula:
Gravitational constant, G = 6.7 × 10^{–11} Nm^{2}/Kg^{2}
Mass of earth, m_{1} = 6 × 10^{24} kg
Mass of ball, m_{2} = 1 kg
Distance between centre of earth and ball
r = Radius of earth
= 6.4 × 10^{3} km
= 6.4 × 10^{3} × 1000m
= 6.4 × 10^{6} 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.
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} Nm^{2} kg^{–2}
Mass of the earth, m_{1} = 6 × 10^{24} kg
Mass of the moon, m_{2} = 7.4 × 10^{22} kg
Distance between Earth and moon
r = 3.84 × 10^{5} km
= 3.84 × 10^{8} km
By putting the values in the formula, we get :
F = 2.01 × 10^{20} newtons
Thus, the gravitational force exerted by the earth on the moon is 2.01 × 10^{20} 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.
Explanation: The formula for calculating the acceleration due to gravity is :
Gravitational constant, G = 6.7 × 10^{–11} Nm^{2}/kg^{2}
Mass of the moon, M = 7.4 × 10^{22} kg
Radius of the moon, R = 1740 km
1.74 × 10^{6} m
Now, putting these values in the formula, we get :
Or g = 1.63 m/s^{2}
Thus, the acceleration due to gravity, g, on the surface of the moon is 1.63 m/s^{2}.
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/s^{2}.
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/s^{2} (stone is coming down)
And, Height of the bridge, h = ?
For a freely falling body :
Height, h = ut + (1/2) gt^{2}
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.