Tag: introduction to gravity

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Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

The gravitational force between two points masses $m _{1}$ and $m _{2}$ at separation $r$ is given by $F=G\dfrac {m _{1}m _{2}}{r^{2}}$ The constant $G$

  1. depends on system of unit only

  2. depends on media between masses only
  3. depends on both $a$ and $b$
  4. is independent of both $a$ and $b$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The gravitational constant G is a universal constant, meaning it does not depend on the system of units or the medium between the masses.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

At what height from the surface of the earth will the value of acceleration due to gravity be reduced by $36\%$ from the value at the surface?
(Radius of earth=$6400\ km$)

  1. $1500\ km$
  2. $1200\ km$
  3. $1000\ km$
  4. $1600\ km$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If g is reduced by 36%, the new g' = 0.64g. Using g' = g * (R / (R+h))^2, we get 0.64 = (R / (R+h))^2, so 0.8 = R / (R+h). Solving for h gives h = 0.25R = 1600 km.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

A cylinderical vessel is filled with equal amount of weight of mercury and water.The overall height of the two layer is 29.2 cm,specific gravity of mercury is 13.6.Then the pressure of the liquid at the bottom of the vessel is:

  1. $29.2 cm$ of water
  2. $\dfrac{29.2}{13.6} cm$ of mercury
  3. $4 cm$ of mercury
  4. $15.6 cm$ of mercury
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
${ M } _{ Hg }={ M } _{ w }$
${ P } _{ Hg }\left( A\times { L } _{ Hg } \right) ={ P } _{ w }\left( A\times { L } _{ w } \right) $
$\therefore$   ${ L } _{ w }=13.6{ L } _{ Hg }$
${ L } _{ w }+{ L } _{ Hg }=29.2$
$\Rightarrow { L } _{ Hg }=2cm\quad \quad { L } _{ w }=27.2cm=2cm$ of $Hg$
Total pressure $=4cm$ of $Hg$.
Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

Two balls, each of radius $R$, equal mass and density are placed in contact, than the force of gravitation between them is proportional to

  1. $F\propto \dfrac {1}{R^{2}} $
  2. $F\propto R $
  3. $F\propto R^{4} $
  4. $F\propto \dfrac {1}{R} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,

Two balls, each of radius $R$ and of equal mass and density, are placed in contact.

  • Step-1:

Find the Distance between the centre of two balls

Distance between the centre of two balls $=$ Sum of their Radii.

Distance between the centre of two balls $= R+R = 2R$.

  • Step-2:

Express the Mass of a ball as product of Density and Volume.

(This would be same for other ball ,given that two balls have equal mass)

Since, the shape of the ball is Sphere.

Volume of the ball $V=\dfrac 43 \pi R^3$

So,

Mass of the ball $m=\rho\times \dfrac 43 \pi R^3$

  • Step-3:

Find the force of gravitation between the two balls.

According to Newton's Law of Universal Gravitation

$F=\dfrac{GMm}{r^2}$

Where,

$F =$ Gravitational Force between two objects.

$G =$ Gravitational constant

$M =$ Mass of the first object

$m =$ Mass of the second object

$r =$ Distance between objects

Here,
.
$M=m=\rho \times \dfrac 43 \pi R^3$

Substituting Values

$\implies F=\dfrac{Gm^2}{(2R)^2}$

$\implies F=\dfrac{G(\rho \times \dfrac 43\pi R^3)^2}{4R^2}$

$\implies F=G\times \rho^2\times (\dfrac 43)^2 \times \dfrac 14\times \dfrac{R^6}{R^2}$

$\implies F=G\times \rho^2\times (\dfrac 43)^2 \times \dfrac 14 \times R^4$

$\implies F\propto R^4$

Therefore,

The force of gravitation between the two balls is proportional to $R^4$
Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

A satellite of the earth is revolving in circular orbit with a uniform velocity V. If the gravitational force suddenly disappears, the satellite will

  1. continue to move with the same velocity in the same orbit.

  2. move tangentially to the original orbit with velocity V.

  3. fall down with increasing velocity.

  4. come to a stop somewhere in its original orbit.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The satellite is revolving around earth because the centripetal force is balanced by earth's gravitational pull.If the gravitational pull disappears, the satellite free of centripetal force. So, it will travel with its instantaneous velocity i.e. in the direction tangential to the circular path.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

A body has a weight $90\ N$ on the earth's surface the mass of the moon is $1/9$ that of the earth's mass and its radius is $1/2$ that of the earth's radius. on the moon the weight of the body is :

  1. $45\ N$
  2. $202.5\ N$`
  3. $90\ N$
  4. $40\ N$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Weight on Moon = W_earth * (M_moon / M_earth) * (R_earth / R_moon)^2. Given M_moon = 1/9 M_earth and R_moon = 1/2 R_earth, Weight = 90 * (1/9) * (2)^2 = 10 * 4 = 40 N.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

If the distance between two bodies is doubles, the force of gravitational attraction between them. 

  1. Becomes four times

  2. Is doubled

  3. Is reduced to one-fourth

  4. Is reduced to half.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Gravitational force is inversely proportional to the square of the distance (F proportional to 1/r^2). If distance is doubled, force becomes 1/(2^2) = 1/4 of the original.