Gravitation Test - 17

If the body displaces liquid whose weight is equal to the actual weight of body, the downward force weight will be balanced by the buoyant force and the body won't experience any net downward force in that case.

$$\textbf{Hint:}$$ Acceleration due to gravity depends on the distance from center of earth.

 $$\textbf{Step1:Acceleration due to gravity on surface of earth}$$

Acceleration due to gravity at surface of Earth is given by,

$$g=\dfrac{GM}{{{R}^{2}}}$$

Where,

$$G$$ is Gravitational constant,

$$M$$ is mass of Earth,

$$R$$ is radius of Earth. 

 

$$\textbf{Step2:Acceleration due to gravity at distance r}$$

Intensity of Gravitational Field or Acceleration due to gravity by mass m at distancre r is given by the formula,

$$g=\dfrac{Gm}{{{r}^{2}}}$$

It is depending on the value of r.

$$\textbf{Step3:Variation in acceleration due to gravity}$$

Let the value of acceleration due to gravity at surface of Earth is $$g$$, and radius of Earth is $$R$$

$$\bullet$$ The value of acceleration due to gravity at height $$h$$ from the surface of Earth is given by the formula,

$$g'=g\left( 1-\dfrac{2h}{R} \right)$$

$$\bullet$$ And the value of acceleration due to gravity at depth $$h$$ from surface of Earth is given by the formula,

$$g'=g\left( 1-\dfrac{h}{R} \right)$$

Thus, its values changes with latitude.

Option C is correct.

If a rock is brought from the surface of the moon, its weight will change, as $$g$$ on earth is 6 times more, but not mass.

A spring balance works due to the stretching of the spring due to the weight of the load added to the balance. Although it is calibrated in terms of mass, it actually measures weight i.e. the gravitational force acting on the load.

Option A is incorrect as all bodies attract each other with force equal to gravitational force

Option B is incorrect as earth behaves like a large magnet 

Option C is incorrect as acceleration due to gravity is $$9.8\; ms^{-2}$$

In option D,since we know, the attractive force F between two bodies of masses $$m_1$$ and $$m_2$$ , separated by distance r is given by $$F = \dfrac{G m_1 m_2 }{ r^2}$$

Considering M as the mass of earth, the acceleration on a particle of mass m would be

$$g = \dfrac{F}{m} = \dfrac{GM}{ r^2}$$.

Since this acceleration is independent of mass of the body, in vacuum, all bodies fall at the same rate under free fall.

The value of g near the earth's surface is 9.8$$m/s^2$$

A moving object will continue to move in a straight line at the same speed unless a force acts on it. For an object to move in a circle, a force has to act on it all the time. This force is called the centripetal force. It acts towards the center of the circle. Gravity is the centripetal force that keeps planets moving around the Sun, and satellites moving around planets.

The gravitational force provides necessary centripetal force for planet to revolve around the sun.

Mass, which is a property of body, remains constant. However, weight varies according to the gravitational force acting between masses.

Sir Newton's gravitational law states that there is always an attraction force exist between any two masses in the universe. Therefore, force of gravitation exists between two astronauts in space .