Gravitation Test

Result

Gravitation Test - 63

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Weekly Quiz Competition

Question 1
1 / -0

The escape velocity on the surface of a planet is $$V_{e}$$ what would be the escape velocity on the planet having the same radius but mass 4 times that of it.

A
2 $$V_{e}$$

B
4 $$V_{e}$$

C
$$V_{e}$$

D
$$\frac{V_{e}}{2}$$

Solution

The equation for the escape velocity of a planet in our solar System is:

v(e)= (2GM/R)^1/2. Your example would change the equation to:

v(e)=(2G*4M/3R)^1/2 so when you cancel the threes you get v(e)=(2GM/R)^1/2 = 2V(e)
Question 2
1 / -0

Spot the wrong statement:
The acceleration due to gravity g decreases if

A
We go down from the surface of the earth towards its centre

B
We go up from the surface of the earth

C
We go from the equator towards the poles on the surface of the earth

D
The rotational velocity of the earth is increased
Question 3
1 / -0

If the acceleration due to gravity, g, is 10 $$m/s ^{2}$$ at the surface of the earth (radius 6400 km), then at a height of 1600 km the value of g will be ( in $$m/s ^{2}$$)

A
6.4

B
5

C
7.5

D
2.5

Solution

Let $$g_e= 10 m/s $$
$$R_e =6400m$$
$$g'=?$$
hence by formula
$$g'-g_e = \dfrac{1}{2}\times \dfrac{h}{R_e}$$
thus g=-4.9 m\s
Question 4
1 / -0

The tilt of Earth is _____ degrees.

A
$$90$$

B
$$23.5$$

C
$$0$$

D
$$35.2$$

Solution
Question 5
1 / -0

The change in the value $$'g'$$ at a height $$'h'$$ above the surface of the earth is the same as at a depth $$'d'$$ below the surface of earth. When both $$'d'$$ and $$'h'$$ are much smaller than the radius of earth, then which one of the fol lowing is correct?

A
$$d=h$$

B
$$d=2h$$

C
$$d=\dfrac {2h}{2}$$

D
$$d=\dfrac {h}{2}$$

Solution

Acceleration due to gravity at a depth 'd' from earth surface is:
$$g_d=g\left(1-\dfrac{d}{R}\right)$$
Acceleration due to gravity at height 'h' from earth surface is: he is very much smaller than R.
$$g_h=g\left(1-\dfrac{2h}{R}\right)$$
$$g_h=g_d$$
By solving it, $$d=2h$$.
Question 6
1 / -0

The value of acceleration due to gravity on earth surface-

A
is directly proportional to density of earth

B
is inversely proportional to density of earth

C
does not depend on density of earth

D
none of these

Solution
Question 7
1 / -0

If the radius of earth shrinks by 1.5 % ( mass remaining same ), then the value of gravitational acceleration changes by

A
2 %

B
-2 %

C
3 %

D
-3 %

Solution

g = G M / R²

as, R is decreased by 1.5%

So, new Radius , R' = R - 0.015 R = 0.985R

So, new g, g' = G M / (0.985R)²

= 1.0306 G M/ R²

So, change = 0.0306

% change = 3 % (approx)
Question 8
1 / -0

A body weighs 144 N at the surface of earth. When it is taken to a height of $$h=3R$$, where R is radius of earth, it would weigh

A
48 N

B
36 N

C
16 N

D
9 N

Solution
Question 9
1 / -0

Assuming the earth to have constant density, point out which of the following curves show variation of acceleration due to gravity from the centre of the point to far away from the surface of the earth.

A

B

C

D
None of these

Solution

If distance from centre of earth = r then $$g ∝ r$$ if $$r < R$$
$$g ∝ \dfrac{1}{r^2}$$ if $$r > R$$.
Question 10
1 / -0

Identify the incorrect statement about a planet revolving around Sun

A
The gravitational attraction provides the centripetal force for a revolving planet

B
The total energy of a planet is always negative

C
The total energy of a planet is always more than potential energy of the system

D
Kinetic energy of revolving planet is sometimes zero

Solution

The total energy of a planet is always negative.
The total energy of a planet is always more than potential energy of the system.
kinetic energy of revolving planet is sometimes zero.
But, the gravitational attraction provides the centripetal force for a revolving planet is incorrect.
Hence, Option $$A$$ is incorrect statement.