Gravitation Test

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Gravitation Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

The gravitational force with which the earth attracts the moon :

A
Is less than the force with which the moon attracts the earth.

B
Is equal to the force with which the moon attracts the earth.

C
Is greater than the force with which the moon attracts the earth

D
Varies with the phases of the moon.
Solution
$$\textbf{Hint:}$$ Newton's law is applicable for all bodies in the whole world.
$$\textbf{Explanation:}$$
- Every thing in the world reacts with equal and opposite force when a force is applied to it, according to Newton's third law. Consider the earth's and moon's systems. The gravitational force pulls all things near the earth, including those that are extremely far away, towards it.
- As a result, the moon draws the earth with the same gravitational force as the earth attracts the moon.
Question 2
1 / -0

Select the wrong statement:
The weight of the floating body is equal to the

A
weight of the displaced liquid.

B
buoyant force acting on the floating body.

C
the weight of the liquid that occupies the portion of the volume of the body that is inside the liquid.

D
the weight of the liquid whose volume is equal to the volume of the part of the body that is above the liquid surface.

Solution

According to Archimedes principle, When a body is floating inside the liquid then force apply by the liquid should be equal to the weight of liquid that is displaced by body. and that is equal to the weight of body.
Statement given in options A,B and C are same that is correct. But statement D is wrong.
hence Correct option is D.
Question 3
1 / -0

Which of the following is the CGS unit of relative density?

A
$$kg m^2 s^{-2}$$

B
$$kg m^{-3}$$

C
$$g cm^{-3}$$

D
None of the above

Solution

The relative density is a ratio of similar quantities, so it has no unit. It is the ratio of the density of a substance to that of water:
Relative density $$=\dfrac{\text{density of a substance}}{\text{density of water}}$$

So option D is correct.
Question 4
1 / -0

A ball is projected vertically up with a velocity of $$20 ms^{-1}$$. Its velocity, when the displacement is $$15 m$$, is......... $$ms^{-1}.$$ (Take $$g = 10 ms^{-2}$$)

A
$$10$$

B
$$15$$

C
$$-10$$

D
Both (A) and (C)

Solution

Given:
Initial velocity $$u=20\ m/s$$
Diaplacement $$s=15\ m$$
Gravitational acceleration $$g=10\ m/s^2$$ (Considering downard direction as positive)
Final velocity $$v=?$$
Using the equation of motion , $$ v^2 = u^2 - 2gh$$
$$ v^2 = 20^2 - 2 \times 10 \times 15$$
$$\Rightarrow v^2=100$$
$$\Rightarrow v=\pm 10\ m/s$$
Since the upward direction is negative, the required velocity is $$ v = -10 m/s$$
Question 5
1 / -0

On the surface of the earth, the force of gravitational attraction between two masses kept at distance $$d$$ apart is $$6$$$$ N$$. If these two masses are taken to the surface of the moon and kept at the same distance $$d$$, the force between them will be:

A
$$1$$$$\ N$$

B
$$36$$$$\ N$$

C
$$\dfrac{1}{6}\ N$$

D
$$6$$$$N$$

Solution

As per Newton's law of gravitation, the force of attraction between two bodies is proportional to the product of the individual masses of the two bodies and inversely proportional to the square of the distance between them. This force will remain same for the two bodies whether they are on the earth or on the moon.
Question 6
1 / -0

A cubical block of wood of side 5 cm is placed on a table. Find the thrust by the block of wood on the table, if density of wood is $$5 g cm^{-3}$$ and g is $$10 m s^{-2}$$

A
4.25 N

B
5 N

C
6.25 N

D
7 N

Solution

Given
Block side $$a=5\ cm$$
Wood density $$d=5\ g/cm^3$$
Volume of the cubical block with side ' a ' cm, $$ v=a^{3} cm ^{3}$$
so volume of cube with side length 5 cm $$= (5 cm ) ^{3} =125 cm^{3}$$

As we know, Density = $$ \dfrac{Mass}{Volume}$$

Mass $$=Density\ \times\ volume$$

so mass of the cube $$M= 5 \times 125 = 625\ g= 0.625\ kg$$

From FBD of table,
Force applied by the block on the table will be equal to the normal force that is equal to $$N$$.

From FBD of block,

$$N=mg=0.625\times 10\ =6.25\ N$$

Hence Thrust force on the table by woodblock will be equal to 6.25 N
so option (C) is correct
Question 7
1 / -0

The base of a cylindrical vessel is $$300\ cm^2$$. Water is poured into it up to a depth of $$6\ cm$$. What will be the thrust acting on the base?
(Take density of water $$\rho_w=1000\ kg/m^{3}$$ and $$g=10\ m/s^{2}$$)

A
$$8\ N$$

B
$$15\ N$$

C
$$18\ N$$

D
$$20\ N$$

Solution

Given,
Height of the cylinder, $$h=6\ cm=0.06\ m$$,
Area of the base,$$A =300\ cm^2=300\times 10^{-4}\ m^2$$
$$A=0.03\ m^2$$
Density of water, $$\rho_w=1000\ kg/m^{3}$$
Acceleration due to gravity, $$g=10\ m/s^{2}$$
Mass of the water filled, $$m$$
We know,
$$Density=\dfrac{mass}{volume}$$
$$\rho =\dfrac mv$$
$$\implies m=\rho \times V$$
$$m=\rho_w\times A \times h$$
$$m=1000\times 0.03\times 0.06$$
$$m= 1.8\ kg$$

Thrust is the force along a particular direction.
Thrust, $$F=m\times g$$
$$F=1.89\times 10$$
$$F=18\ N$$
Question 8
1 / -0

Difference between mass and weight.

A
Weight is a force where as mass is not a force.

B
The mass of an object is always more than its weight.

C
Mass can be expressed only in the metric system.

D
There is no difference.

Solution

Weight is the gravitational force acting on the body.
Mass is the amount of matter the body contains.
Relation between weight and mass is
$$ w = mg$$
So, Option A is correct.
Question 9
1 / -0

The value of g on the moon is $$\dfrac {1}{6}th$$ that on earth. A body weighing 60 kg on the earth has weight on the moon equal to?

A
20 kg

B
Zero

C
360 kg

D
10 kg

Solution

Given,
Mass of body on earth $$m_e=60\ kg$$
Value of g on moon $$g_m=\dfrac16g_e$$ where $$g_e, \ g_m$$ gravitational acceleration on earth and moon respectively.

Weight of body on earth $$W_e=mg_e=60 g_e$$
Weight of body on moon $$W_m=mg_m=60 g_m=60\times \dfrac16g_e=10g_e$$

Reading of same weighing machine on moon $$=\dfrac{Weight\ of\ object\ on\ moon }{g_e}=\dfrac{10\ g_e}{g_e}=10\ kg$$

Option D
Question 10
1 / -0

A rectangular tank of 6 m long, 2 m broad and 2 m deep is full of water, the thrust acting on the bottom of the tank is:

A
$$23.52\times 10^4N$$

B
$$23.512 N$$

C
$$11.76\times 10^4 N$$

D
$$3.92\times 10^4 N$$

Solution

volume of tank = $$ 6\times2\times2=24 cm^{3}$$
$$F_{thrust}$$ = $$\rho gh\times area$$ ( as force = pressure (area) )
= $$1000\times 9.8\times 24$$ ( as area $$\times$$ height = volume)
=$$23.52 \times 10^{4} N$$
so option (A) would be correct

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Gravitation Test - 38

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Gravitation Test - 38

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SHARING IS CARING

Question 1

Is less than the force with which the moon attracts the earth.

Is equal to the force with which the moon attracts the earth.

Is greater than the force with which the moon attracts the earth

Varies with the phases of the moon.

Solution

Question 2

weight of the displaced liquid.

buoyant force acting on the floating body.

the weight of the liquid that occupies the portion of the volume of the body that is inside the liquid.

the weight of the liquid whose volume is equal to the volume of the part of the body that is above the liquid surface.

Solution

Question 3

$$kg m^2 s^{-2}$$

$$kg m^{-3}$$

$$g cm^{-3}$$

None of the above

Solution

Question 4

$$10$$

$$15$$

$$-10$$

Both (A) and (C)

Solution

Question 5

$$1$$$$\ N$$

$$36$$$$\ N$$

$$\dfrac{1}{6}\ N$$

$$6$$$$N$$

Solution

Question 6

4.25 N

5 N

6.25 N

7 N

Solution

Question 7

$$8\ N$$

$$15\ N$$

$$18\ N$$

$$20\ N$$

Solution

Question 8

Weight is a force where as mass is not a force.

The mass of an object is always more than its weight.

Mass can be expressed only in the metric system.

There is no difference.

Solution

Question 9

20 kg

Zero

360 kg

10 kg

Solution

Question 10

$$23.52\times 10^4N$$

$$23.512 N$$

$$11.76\times 10^4 N$$

$$3.92\times 10^4 N$$

Solution

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