Question

proper explanation required for both.​

Answer 1

$\large\mathcal{\underbrace{\red{SOLUTION:-}}}$

(i) ANSWER :- ‘g/4’ .

EXPLANATION :-

$\bigstar\:\rm{\purple{\boxed{g'\:=\:\dfrac{g}{(1\:+\:\dfrac{h}{R})^2}\:}}}$

✍️ Here,

• h = R

$\rm{\implies\:g'\:=\:\dfrac{g}{(1\:+\:\dfrac{R}{R})^2}\:}$

$\rm{\implies\:g'\:=\:\dfrac{g}{(1\:+\:1)^2}\:}$

$\checkmark\:\rm{\blue{\boxed{\implies\:g'\:=\:\dfrac{g}{4}\:}}}$

________________________________

(ii) ANSWER :- 200N .

EXPLANATION :-

✍️ Weight of the body on the surface of Earth = 450 N .

=> mg = 450N

=> m × 10m/s² = 450N

=> m = 45kg .

Now,

✔️ Mass of planet = 1/9 mass of Earth .

$\rm{\red{\underline{\implies\:m_p\:=\:\dfrac{1}{9}\:m_e\:}}}$

✔️ Radius of planet = 1/2 Radius of Earth

$\rm{\red{\underline{\implies\:R_p\:=\:\dfrac{1}{2}\:R_e\:}}}$

✍️ Value of gravity on earth is,

$\checkmark\:\rm{\orange{g_e\:=\:\dfrac{G\:m_e}{R^2_e}\:}}$

✍️ Value of gravity on planet is,

$\checkmark\:\rm{\purple{g_p\:=\:\dfrac{G\:m_p}{R^2_p}\:}}$

$\rm{\implies\:g_p\:=\:\dfrac{G\:{\dfrac{m_e}{9}}}{(\dfrac{R_e}{2})^2}\:}$

$\rm{\implies\:g_p\:=\:\dfrac{4}{9}\:\times\:\dfrac{G\:m_e}{R^2_e}\:}$

$\rm{\green{\implies\:g_p\:=\:\dfrac{4}{9}\:g_e\:}}$

✍️ Now, weight on the planet is = $\rm{m\:g_p}$

$\rm{\implies\:Weight\:on\:planet\:=\:45\times{\dfrac{4}{9}}\times{10}\:}$

$\rm{\pink{\implies\:Weight\:on\:planet\:=\:200\:N}}$

Answer 2

Answer:

i) The acceleration due to gravity at a height is given by

                g'=g(1-2h/R)

                    =g(1-2R/R)

                    =g(1-2)

                    =-g = -9.8 m/s²

    ∴the acceleration due to gravity at height R is -9.8 m/s²

ii) the acceleration due to gravity is given by

           g=GM/R²  (where G is the gravitation constant, M is mass of earth)

     In the question,

                          M'=M/9 -----(1)

                          R'=R/2 -----(2)

       Subsituting these on the equation,

         g'=G(M/9)/(R/2)²

            =(4/9)GM/R²

         g'=(4/9)g                 (∵g=GM/R²)

    Weight on earth W=mg

                               450=m×10  (for simplicity, g=10 m/s²)

                          ∴m=45 kg

   ∴Weight on the planet W'=mg

                                              =45×40/9

                                              =45×4.44

                                              =199.8 kg wt

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