Question

3. The mass of a body is 40 kg. Find the weight of the body on the surface of a planet whose mass is double
than the mass of the earth and radius is 4 times the radius of the earth. ​

Answer 1

Answer:

Given:

Mass of planet is double as that of Earth, radius is 4 times as that of Earth. Mass = 40 kg.

To find:

Weight of a body on that planet.

Concept:

Weight is given as the product of mass and gravitational acceleration.

Now the gravity changes on different planets on the basis of mass and radius of planets. Hence the weight on that planet will change .

Calculation:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{ \red{g = \dfrac{GM}{ {r}^{2} }}}}$

Now Earth :

$g_{e} = \dfrac{GM}{ {r}^{2} }$

For that planet :

$g_{p} = \dfrac{G(2M)}{ {(4r)}^{2} }$

$\implies g_{p} = \dfrac{1}{8} ( \dfrac{GM}{ {r}^{2} } )$

$\implies \: g_{p} = \dfrac{1}{8} (g_{e})$

So weight on that planet :

$weight = 40 \times \{ \frac{1}{8}g_{e} \}$

$\implies weight = 40 \times \dfrac{10}{8}$

$\implies weight = 50 \: N$

So final answer :

$\boxed{ \huge{ \sf{ \red{ weight = 50 \: N}}}}$

Answer 2

$\boxed{ \bold{ \orange{ \sf{ \huge{Answer}}}}} \\ \\ \star \sf \: \red{Given} \\ \\ \implies \sf \: mass \: of \: body \: (M) = 40 \: kg \\ \\ \implies\sf \: a \: planet \: whose \: mass \: is \: double \: than \: mass \: of \: earth \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: and \: radius \: is \: four \: time \: radius \: of \: earth. \\ \\ \star \sf \: \red{To \: Find} \\ \\ \implies \sf \: weight \: of \: the \: body \: on \: that \: surface \\ \\ \star \sf \: \red{Formula} \\ \\ \implies \sf \: weight \: of \: body \: is \: given \: as... \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{ \sf{ \blue{W = M \times g}}}} \\ \\ \implies \sf \: where \: g \: is \: gravitational \: acceleration \: \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: of \: planet \\ \\ \implies \sf \: gravitational \: acceleration \: of \: the \: planet \: \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: is \: given \: as... \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{ \sf{ \blue{g = \frac{GM}{ {R}^{2} }}}}} \\ \\ \implies \sf \: where \: G = gravitational \: constant \\ \\ \implies \sf \: let \\ \\ \sf \: mass \: of \: earth \: is \: M1 \: and \: radius \: is \: R1 \\ \\ \sf \: mass \: of \: other \: planet \: is \: M2 \: and \: radius \: is \: R2 \\ \\ \sf \: gravitational \: acceleration \: of \: earth = g1 = 10 \: \frac{m}{ {s}^{2} } \\ \\ \sf \: gravitational \: acceleration \: of \: other \: planet = g2 \\ \\ \star \sf \: \red{Calculation} \\ \\ \implies \sf \: \frac{g1}{g2} = \frac{M1 \times ({R2)}^{2} }{M2 \times {(R1)}^{2} } = \frac{M1 \times {(4R1)}^{2} }{(2M1) \times {R1}^{2} } = 8 \\ \\ \implies \sf \: g2 = \frac{g1}{8} = \frac{10}{8} = 1.25 \: \frac{m}{ {s}^{2} } \\ \\ \implies \sf \: Weight = M \times g2 = 40 \times 1.25 = 50 \: N \\ \\ \boxed{ \boxed{ \bold{ \sf{ \huge{ \green{Weight = 50 \: N}}}}}}$