Gravitation Worksheet-5
A. 1/4 times B. 1/2 times C. 4 times D. 2 times
A. Depends on the value of g at the place of observation
B. Is used only when the earth is one of the two masses
C. Is the greatest on the surface of the earth
D. Is of the same value irrespective of the place of observation
A. x/4 B. x/2 C. 2x D. 4x
A. F_{1} is very much greater than F_{2}
B. F_{2} is very much greater than F_{1}
C. F_{1} is only a little greater than F_{2}
D. F_{1} and F_{2} are exactly equal
A. r^{2} ∝ T^{3} B. r ∝ T^{2} C. r^{3} ∝ T^{2} D. r^{3} ∝ (1/T^{2})
A. 50 N/ m^{2} B. 200 N/ m^{2} C. 50 N/m D. 25 N/ m^{2}
A. 5000,000 Pa B. 20 Pa
C. 1/20 Pa D. 5000,00 Pa
(a) When the wooden block is kept with its surface measuring 50 cm × 25 cm on the table.
(Assume : Acceleration due to gravity, g = 10 m/s^{2})
A. 320 pascals B. 0.320 pascals
C. 3.20 pascals D. 32.0 pascals
A. 50 N B. 25 N C. 1/2 N D. 2 N
A. 7800 kg/ m^{3}. B. 31200 kg/ m^{3}.
C. 15600 kg/ m^{3}. D. 780 kg/ m^{3}.
Answer Key:
Explanation: The force between two bodies is directly proportional to the product of their masses.
That is, F ∝ m_{1} × m_{2}
If masses of both the bodies are doubled then the force will become 4 times.
Explanation: G is gravitational constant.
Explanation: (i) The force between two bodies is directly proportional to the product of their masses.
That is, F ∝ m_{1} × m_{2} …. (1)
(ii) The force between two bodies is inversely proportional to the square of the distance between them.
That is, ... (2)
Combining (1) and (2), we get:
Gravitational force,
If distance is r/2 then the force will be 4 times.
Explanation: Here, Force = 100 N
And, Area = 2 m^{2}
Now, putting these values in the formula :
We get:
= 50 N/ m^{2} (or 50 Pa)
Thus, the pressure is 50 newtons per square metre or 50 pascals.
Explanation: In this case the force will be the weight of woman which is given by m x g (where m is the mass of woman and g is the acceleration due to gravity).
So, Force = m × g
(Weight of woman) = 50 × 10 N
= 500 N
And, Area = 1 cm^{2}
Now,
= 5000,000 N/m^{2} (or 5000,000 Pa)
Thus, the pressure exerted by woman is 5000,000 N m^{2}.
Explanation: Here, Mass of wooden block, m = 4 kg
Acceleration due to gravity, g = 10 m/s^{2}
So, weight of wooden block, W = m × g
= 4 × 10
= 40 N
Since weight is a force, so we can say that the force exerted by the wooden block on the table top is 40 N. We will now calculate the pressure in the two cases.
And, Area = 50 cm × 25 cm
= 0.125 m^{2}
Now,
= 320 N m^{–2} (or 320 Pa)
Thus, the pressure exerted by the wooden block on table top when kept on its face measuring 50 cm x 25 cm is 320 N m^{–2} or 320 pascals
Explanation: According to Archimedes' principle, the buoyant force acting on this object will be equal to the weight of water displaced by this object. So, we have to find the weight of water displaced in 'newtons'. That will give us the buoyant force. We know that :
Weight, W = m x g
Here, Mass of water, m = 5 kg
And, acceleration due to gravity g = 10 m/s^{2}
Weight of water, W = 5 × 10 N = 50 N
Now, since the weight of water displaced by the object is 50 newtons, therefore, the buoyant force acting on the object (due to water) will also be 50 newtons.
Explanation: We know that :
= 7800 kg/m^{3}
Thus, the density of steel in SI units is 7800 kg/ m^{3}.