Question

$\huge\mathcal\color{teal} Question :-$

ɪғ ᴛᴡᴏ ᴏʙᴊᴇᴄᴛs ᴏғ 1 ᴋɢ ᴍᴀss ᴀʀᴇ ʟᴏᴄᴀᴛᴇᴅ ɪɴ sᴘᴀᴄᴇ ᴀᴛ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 1 ᴍᴇᴛᴇʀ, ᴛʜᴇɴ ʜᴏᴡ ʟᴏɴɢ ᴡɪʟʟ ɪᴛ ᴛᴀᴋᴇ ғᴏʀ ᴛʜᴇᴍ ᴛᴏ ᴄᴏᴍᴇ ᴛᴏɢᴇᴛʜᴇʀ?​

Answer 1

Given :

➳ Mass of each object = 1kg

➳ Distance b/w them = 1m

To Find :

➠ Time taken by them to come together.

SoluTioN :

➛ Both objects are placed in space therefore they will attract each other. (Due to Gravitational force)

➛ Here, only Gravitational force acts between them therefore they come towards each other.

✭ Gravitational Force :

⇒ F = GMm/R² (M = m = 1kg)

⇒ F = G(1)(1)/(1)²

⇒ F = G N

✭ Acceleration of each object :

⇒ F = ma

⇒ ma = G

⇒ a = G/m

⇒ a = G/(1)

⇒ a = G m/s²

➢ Here, Acceleration is constant throughout the motion, we can apply second equation of kinematics to calculate time taken by them to come together.

[Note : Total distance covered by each particle will be 0.5m]

✭ Calculation of time :

➾ s = ut + (1/2)at²

➾ 0.5 = (0 × t) + 0.5Gt²

➾ Gt² = 0.5/0.5

➾ t² = 1/G

➾ t² = $\sf{\dfrac{1}{6.67\times 10^{-11}}}$

➾ t = $\sf{\sqrt{1.499\times 10^{10}}}$

➾ $\underline{\boxed{\bf{\purple{t=1.22\times 10^5\:s}}}}\:\gray{\bigstar}$

Answer 2

Explanation:

Time taken by them to come together.

SoluTioN :

➛ Both objects are placed in space therefore they will attract each other. (Due to Gravitational force)

➛ Here, only Gravitational force acts between them therefore they come towards each other.

u r answer is

t=1.22×10⁵s

it is help ful to mark me as brilliant