Question

Earth gravitational pull causes and acceleration of 7 metre per second square in 2 kg of a body somewhere in space how much will be the acceleration of 10 kg of mass due to Earth's gravitational pull on the same object​

Answer 1

Given:

Earth gravitational pull causes and acceleration of 7 m/s² in 2 kg of a body somewhere in space.

To find:

Acceleration of 10 kg mass due to gravitational pull of Earth at that same point.

Calculation:

Acceleration is given by the ratio of force and the mass of the object.

For the 2kg body ; let acceleration be a1:

$a1 = \dfrac{force}{mass}$

$= > a1 = \dfrac{ (\frac{GMm}{ {d}^{2} } )}{m}$

$= > a1 = \dfrac{GM}{ {d}^{2} } = 7 \: m {s}^{ - 2} \: \: .........(1)$

For the 10 kg body ; let acceleration be a2:

$a2 = \dfrac{force}{mass}$

$= > a2 = \dfrac{ \{\frac{GM(m2)}{ {d}^{2} } \}}{(m2)}$

$= > a2 = \dfrac{GM}{ {d}^{2} } \: \: .............(2)$

So , we can say that :

$\boxed{ \sf{a1 = a2 = 7 \: m {s}^{ - 2} }}$

So , the 10 kg object will also be pulled by the same acceleration of 7 m/s².