Gravitation Test

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Gravitation Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

The energy required to remove a body of mass 'm' from earths surface is/are equal to:

A
-GMm/R

B
mgR

C
-mgR

D
none of these.

Solution

Potential energy required to remove a body of mass $$m$$ from earth's surface is $$mgR$$
Question 2
1 / -0

The escape velocity of projection from the earth is approximately ($$R = 6400 km$$).

A
$$7 km/s$$

B
$$112 km/s$$

C
$$11.2 km/s$$

D
$$1.1 km/s$$

Solution

$$V_{escape}=\sqrt{\cfrac{2GM}{R}}$$
$$=\sqrt{\cfrac{2(6.67\times 10^{-11}\times 5.98\times 10^{24})}{6.38\times 10^{6}}}ms^{-1}$$
$$=\sqrt{1.251\times 10^8} ms^{-1}$$
$$=11184 ms^{-1}$$
$$\approx 11.2 Kms^{-1}$$
Question 3
1 / -0

The earth retains its atmosphere because

A
The earth is sphere

B
The earth has population

C
The escape velocity of molecules is less than the mean speed of molecules

D
The escape velocity of molecules is more than the mean speed of molecules

Solution

The earth have atmosphere because earths escape velocity is move than mean speed of gaseous molecules, due to this reason gas can't escape.
Question 4
1 / -0

Two identical spherical masses are kept at some distance. Potential energy when a mass $$m$$ is taken from the surface of one sphere to the other

A
increases continuously

B
decreases continuously

C
first increases, then decreases

D
first decreases, then increases

Solution

Centre point is unstable equilibrium position where potential energy is maximum.
(c) first increases then decreases
Question 5
1 / -0

The weight of a body of mass $$3kg$$ at a height of $$12.8 \times 10^6m$$ from the surface of the earth is _______.

A
$$9.75N $$

B
$$1.46N $$

C
$$3.26N $$

D
$$4.36N $$

Solution

Given,
$$Mass=3kg$$
$$,h=128\times10^8=12.8\times10^7 \ m $$
$$R=6.4\times10^6 \ m$$
So, $$ h = 12.8\times10^6=2R$$
$$g'=g_m(\dfrac{R}{R+h})^2=9.8(\dfrac{R}{R+2R})^2=9.8(\dfrac{1}{3})^2=\dfrac{9.8}{9}$$
Thus the weight,
$$W=mg'=3\times \dfrac{9.8}{9}=3.26N$$
Question 6
1 / -0

Gravitational potential energy is negative. This implies

A
Energy is rising along negative x axis

B
A particle is trapped in this potential

C
The particle is moving in the opposite direction

D
Energy is decreasing in the direction of motion of the particle

Solution

Negative gravitational potential energy implies the particle is being bounded by the potential

The correct option is (b)
Question 7
1 / -0

The weight of an astronaut in outer space is

A
Less than his actual weight

B
more than his actual weight

C
same as his actual weight

D
zero

Solution
Question 8
1 / -0

The value of $$'g'$$ will be $$1$$% of its value at the surface of the earth at a height of $$(R_e = 6400km)$$ -

A
6400 km

B
57600 km

C
12560 km

D
64000 km

Solution

$${g^1} = g\left( {1 - {h \over R}} \right)$$
$$g = g\left( {1 - {h \over R}} \right)$$

$$1 = {h \over R},h = R$$
Question 9
1 / -0

If $$R$$ is the radius of the earth, then the value of acceleration due to gravity at a height $$h$$ from the surface of the earth will become half its value on the surface of the earth if

A
$$h = 2R$$

B
$$h = R$$

C
$$h = (\sqrt {2} + 1)R$$

D
$$h = (\sqrt {2} - 1)R$$

Solution

$$ g^{1} = \dfrac{Gm}{(R+h)^{2}} ...(1) $$ & at surface $$ g = \dfrac{Gm}{R^{2}} ...(2) $$
given that $$ g^{1} = g/2 $$
(1)/(2) we get $$ \dfrac{g^{1}}{g} = \dfrac{R^{2}}{(R+h)^{2}} $$
Put $$ g^{1} = g/2 $$ we get $$ \dfrac{1}{2} = \dfrac{R^{2}}{(R+h)^{2}} $$
$$ \Rightarrow \sqrt{2} = \dfrac{R+h}{R} = 1+\dfrac{h}{R} $$
$$ \Rightarrow \dfrac{h}{R} = \sqrt{2}-1 \Rightarrow h = R(\sqrt{2}-1) $$
Question 10
1 / -0

If the distance between the earth and sun were to be doubled from its present value, the number of days in a year would be :

A
64.5

B
1032

C
182.5

D
730

Solution

Given,

Radius of rotation become double, $${{a}_{2}}=2{{a}_{1}}$$

By Kepler’s law, $$T ^ { 2 }$$$$\alpha \,\,{{a}^{3}}$$

$$\dfrac { T _ { 1 } ^ { 2 } } { a _ { 1 } ^ { 3 } }$$$$= \dfrac { T _ { 2 } ^ { 2 } } { a _ { 2 } ^ { 3 } }$$

$$T _ { 2 } ^ { 2 }$$$$= \left( \dfrac { a _ { 2 } } { a _ { 1 } } \right) ^ { 3 } \times T _ { 1 } ^ { 2 }$$

$$T _ { 2 } ^ { 2 }$$ $$={{\left( \dfrac{2}{1} \right)}^{3}}\times T_{1}^{2}$$

$$T _ { 2 } ^ { 2 }$$ $$=8\times T_{1}^{2}$$

$$T _ { 2 } ^ { 2 }$$ $$=\sqrt{8}\times 365\text{ days }$$

$${{T}_{2}}=1032.37\text{ days }$$

Hence, $$1032$$ days in year.

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Re-Attempt Weekly Quiz Competition

Gravitation Test - 23

Result

Gravitation Test - 23

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SHARING IS CARING

Question 1

-GMm/R

mgR

-mgR

none of these.

Solution

Question 2

$$7 km/s$$

$$112 km/s$$

$$11.2 km/s$$

$$1.1 km/s$$

Solution

Question 3

The earth is sphere

The earth has population

The escape velocity of molecules is less than the mean speed of molecules

The escape velocity of molecules is more than the mean speed of molecules

Solution

Question 4

increases continuously

decreases continuously

first increases, then decreases

first decreases, then increases

Solution

Question 5

$$9.75N $$

$$1.46N $$

$$3.26N $$

$$4.36N $$

Solution

Question 6

Energy is rising along negative x axis

A particle is trapped in this potential

The particle is moving in the opposite direction

Energy is decreasing in the direction of motion of the particle

Solution

Question 7

Less than his actual weight

more than his actual weight

same as his actual weight

zero

Solution

Question 8

6400 km

57600 km

12560 km

64000 km

Solution

Question 9

$$h = 2R$$

$$h = R$$

$$h = (\sqrt {2} + 1)R$$

$$h = (\sqrt {2} - 1)R$$

Solution

Question 10

64.5

1032

182.5

730

Solution

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