Question

Two lead spheres each of 500g are kept with their centres 1 m apart. Find the gravitational force with wiyh they attract each other ​

Answer 1

Given:

Mass of 1st body (1st lead sphere) = 500g =

Mass of 2nd body (2nd lead sphere) = 500g

Distance between them = 1m

To find :

The gravitational force between the two bodies.

According to the Newton's formula of Univeral law of gravational force,

$\rm F_g = G\frac{mM}{r}$

Where,

F = force between the two objects

G = Gravitational Constant = $\rm 6.673 \times 10^{-11} Nm^2/kg^2.$

m = mass of 1st body

M = mass of 2nd body

r = distance between the two points of center of these objects.

Here,

F = ?

G = $\bf \rm 6.673 \times 10^{-11} Nm^2/kg^2$

m = 500g = 0.5 kg

M = 500g = 0.5 kg

r = 1m

Putting the values,

$\therefore \rm F = 6.673 \times 10^{-11} \times \frac{0.5 \times 0.5}{1} \\ \\ \implies \rm F = 6.673 \times 10^{-11} \times 0.25 \\ \\ \implies \bf \rm \red{F = 1.66825 \times 10^{-11}N}$

$\bold{\purple{\textrm{Hence, the force between the two}}} \\ \bold{\purple{\textrm{bodies is}}} \: \bf \rm \red{1.66825 \times 10^{-11}Newton}$

Answer 2

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

$1.66 \times {10}^{ - 11} n$

$\red{\mid{\underline{\overline{\textbf{explanation}}}\mid}}$

According to universal law of gravitation, the force of gravitation between two bodies is directly proportional to product of their masses and inversely proportional to the square of distance between them . This law can be defined by the expression :

${\huge{\boxed{\mathcal{\orange{f = G \frac{Mm}{ {d}^{2} } }}}}}$

In this expression :

• F= Gravitational force between bodies
• M = mass of first body
• m = mass of second body
• d = distance between them.
• G = Universal gravitational constant

For this case :

$\bigstar \: \: \blue{\mid{\underline{\overline{\textbf{We have been given :-}}}\mid}}$

M = 500g = 0.5kg

m = 509g = 0.5kg

d = 1m

F = ?

G = Universal gravitational constant = 6.673 × 10^-11nm^2/kg^2

Now after inputting the given values in the equation we get :

$f = \frac{6.673 \times {10}^{ - 11} \times 0.5 \times 0.5}{ {1}^{2} }$

$f = 6.673 \times {10}^{ - 11} \times 0.25$

${{\boxed{\mathcal{\orange{f =1.66 \times {10}^{ - 11} newton}}}}}$

Therefore the force of attraction or force of gravitation between the given spheres is 1.66× 10^-11N.

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BY SCIVIBHANSHU

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