Question

Answer the question in the attachment

Give relevant answer only

Do full solution ​

Answer 1

Answer:

Option C is the correct answer

Solution :

F =G m1m2

-----------

d^2

So , if we look at option C

F =G (m1/2)(m2/2)

--------------------------

(d/2)^2

= G ( m1m2/4)

-------------------

(d^2/4)

= G m1m2

----------------

d^2

= Gmm

---------------

d^2

And on comparing we see its still the same!

Regards

Answer 2

Solution:-

Formula

$\rm \implies \: F = G \dfrac{m _{1}m_{2} }{ {r}^{2} }$

Now we have to find the gravitational force

Given:-

$\rm \implies \: m_{1} = m$

$\rm \implies m_{2} = m$

$\rm \implies \: r = d$

Now put the value on formula

$\rm \implies \: F = G \dfrac{m \times m }{ {d}^{2} }$

$\rm \implies \: F = \dfrac{m {}^{2} G }{ {d}^{2} }$

Now we have find the same value of F in given below

Now Take one by one

Option:- 1

Given:-

$\rm \implies \: m_{1} = m$

$\rm \implies m_{2} = m$

$\rm \implies \: r = \dfrac{d}{2}$

Now put the value on formula

$\rm \implies \: F = G \dfrac{m \times m }{ \bigg( { \dfrac{d}{2} \bigg)}^{2} }$

$\rm \implies \: F = G \dfrac{m {}^{2} }{ { \dfrac{d}{4} }^{2} }$

$\rm \implies \: F = \dfrac{4m {}^{2} G }{ {d}^{2} }$

Option:-2

Given

$\rm \implies \: m_{1} = \dfrac{m}{2}$

$\rm \implies m_{2} = \dfrac{m}{2}$

$\rm \implies \: r = 2d$

Put the value on formula

$\rm \implies \: F = G \dfrac{ \dfrac{m}{2} \times \dfrac{m}{2} }{(2 {d})^{2} }$

$\rm \implies \: F = G \dfrac{m^{2} }{ 4 \times 4{d}^{2} } =\dfrac{ {m}^{2} G }{16 {d}^{2} }$

Option:- 3

Given

$\rm \implies \: m_{1} = \dfrac{m}{2}$

$\rm \implies m_{2} = \dfrac{m}{2}$

$\rm \implies \: r = \dfrac{d}{2}$

Put the value on formula

$\rm \implies \: F = G \dfrac{ \dfrac{m}{2} \times \dfrac{m}{2} }{ \bigg( { \dfrac{d}{2} } \bigg) ^{2} }$

$\rm \implies \: F = G \dfrac{ {m} {}^{2} }{ { 4 \times \dfrac{d}{4} } ^{2} } = \dfrac{ {m}^{2}G }{ {d}^{2} }$

Option:- 4

Given

$\rm \implies \: m_{1} = 2{m}{}$

$\rm \implies \: m_{2} = 2{m}$

$\rm \implies \: r = \dfrac{d}{4}$

Put the value on formula

$\rm \implies \: F = G \dfrac{2m \times 2m }{ { \bigg(\dfrac{d}{4} \bigg) }^{2} }$

$\rm \implies \: F = G \dfrac{4m {}^{2} }{ { \dfrac{d}{16} }^{2} } = \dfrac{64 {m}^{2} }{ {d}^{2} }$

We can clearly see option 3 is same

Answer

$\rm \to \: correct \: option \: is \: c$