Gravitation Worksheet-5

Gravitation Worksheet-5

 

  1. Two particles are placed at some distance from each other. If, keeping the distance between them unchanged, the mass of each of the two particles is doubled, the value of gravitational force between them will become :

A. 1/4 times      B. 1/2 times      C. 4 times          D. 2 times

 

  1. In the relation F = G × M × m/d2, the quantity G :

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

 

  1. The gravitational force of attraction between two objects is x. keeping the masses of the objects unchanged, if the distance between the objects is halved, then the magnitude of gravitational force between them will become :

A. x/4                 B. x/2                 C. 2x                   D. 4x

 

  1. An apple of mass 100 g falls from a tree because of gravitational attraction between the earth and the apple. If the magnitude of force exerted by the earth on the apple be F1 and the magnitude of force exerted by the apple on the earth be F2, then :

A. F1 is very much greater than F2

B. F2 is very much greater than F1

C. F1 is only a little greater than F2

D. F1 and F2 are exactly equal

 

  1. According to one of the kepler’s laws of planetary motion :

A. r2 ∝ T3          B. r ∝ T2            C. r3 ∝ T2          D. r3 ∝ (1/T2)

 

  1. A force of 100 N is applied to an object of area 2m2. Calculate the pressure.

A. 50 N/ m2      B. 200 N/ m2    C. 50 N/m         D. 25 N/ m2         

 

  1. A woman is wearing pencil-heeled shoes. If the mass of this woman is 50 kg and the area of one heel is 1cm2, calculate the pressure exerted on the ground when the woman stands on just one heel. (g = 10 m/s2).

A. 5000,000 Pa                            B. 20  Pa

C. 1/20 Pa                                      D. 5000,00 Pa

 

  1. A rectangular wooden block has mass of 4 kg. The length, breadth and height of this wooden block are 50 cm, 25 cm and 10 cm, respectively. Find the pressure on the table top:

(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/s2)

A. 320 pascals                              B. 0.320 pascals

C. 3.20 pascals                             D. 32.0 pascals

 

  1. When an aluminium object is immersed in water, it displaces 5 kg of water. How much is the buoyant force acting on the aluminium object in newtons? (g = 10 m/s2).

A. 50 N               B. 25 N               C. 1/2 N             D. 2 N

 

  1. The mass of 2m3 of steel is 15600 kg. Calculate the density of steel in SI units.

A. 7800 kg/ m3.                            B. 31200 kg/ m3.

C. 15600 kg/ m3.                          D. 780 kg/ m3.

 

Answer Key:

  1. C

Explanation: The force between two bodies is directly proportional to the product of their masses.

That is, F ∝ m1 × m2

If masses of both the bodies are doubled then the force will become 4 times.

 

  1. D

Explanation: G is gravitational constant.

 

  1. D

Explanation: (i) The force between two bodies is directly proportional to the product of their masses.

That is, F ∝ m1 × m2                   …. (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.

 

  1. D

 

  1. C

 

  1. A

Explanation: Here, Force = 100 N

And, Area = 2 m2

Now, putting these values in the formula :

         

We get:

                   = 50 N/ m2 (or 50 Pa)

Thus, the pressure is 50 newtons per square metre or 50 pascals.

 

  1. A

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 cm2

                  

Now,

         

          = 5000,000 N/m2 (or 5000,000 Pa)

Thus, the pressure exerted by woman is 5000,000 N m2.

 

  1. A

Explanation: Here, Mass of wooden block, m = 4 kg

Acceleration due to gravity, g = 10 m/s2

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 m2

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

 

  1. A

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/s2

          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.

 

  1. A

Explanation: We know that :

         

          = 7800 kg/m3

Thus, the density of steel in SI units is 7800 kg/ m3.