Question

which object has the greatest weight
an object of mass 10kg in a 15N/kg gravionational field
an object of mass 15kg in a 13N/kg gravionational field
an object of mass 20kg in a 9.0N/kg gravionational field
an object of mass 50kg in a 3.0/kg gravionational field​

Answer 1

Solution :

Formula to be used :

⇒ Gravitational field strength = Weight/Mass

Now for 1st object :-

Mass = 10 kg

Gravitational field strength = 15N/kg

Weight, W₁ = ?

Substituting all values,

⇒ 15N/kg = W₁/10kg

⇒ W₁ = 15N/kg × 10kg

⇒ W₁ = 150N

Now for 2nd object :-

Mass = 15kg

Gravitational field strength = 13N/kg

Weight, W₂ = ?

Substituting all values,

⇒ 13N/kg = W₂/15kg

⇒ W₂ = 13N/kg × 15kg

⇒ W₂ = 195N

Now for 3rd object :-

Mass = 20kg

Gravitational field strength = 9N/kg

Weight, W₃ = ?

Substituting all values,

⇒ 9N/kg = W₃/20kg

⇒ W₃ = 9N/kg × 20kg

⇒ W₃ = 180N

Now for 4th object :-

Mass = 50kg

Gravitational field strength = 3N/kg

Weight, W₄ = ?

Substituting all values,

⇒ 3N/kg = W₄/50kg

⇒ W₄ = 3N/kg × 50kg

⇒ W₄ = 150N

Now, by comparing the weights of all 4 objects, we can say that 2nd object has the greatest weight. (195N)

Thus, 2nd object which is of mass 15kg and gravitational field strength of 13N/kg has the greatest weight among all the 4 objects.

Answer 2

Given :

Which object has the greatest weight :

• 1.) Mass = 10 kg ; Gravitational field = 15 N/kg
• 2.) Mass = 15 kg ; Gravitational field = 13 N/kg
• 3.) Mass = 20 kg ; Gravitational field = 9 N/kg
• 4.) Mass = 50 kg ; Gravitational field = 3 N/kg

$\\ {\underline{\rule{200pt}{3pt}}}$

To Find :

• Object having greatest weight = ?

$\\ {\underline{\rule{200pt}{3pt}}}$

Solution :

⚝ Formula Used :

$\large{\color{cyan}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}}}$

⚝ Let the Weights :

• ➙ ${\sf{ W_1 = Weight \: of \: first \: Object }}$
• ➙ ${\sf{ W_2 = Weight \: of \: second \: Object }}$
• ➙ ${\sf{ W_3 = Weight \: of \: third \: Object }}$
• ➙ ${\sf{ W_4 = Weight \: of \: fourth \: Object }}$

$\qquad{\rule{150pt}{1pt}}$

⚝ Calculating the Weights :

• Weight of 1st Object :

${:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 15 = \dfrac{W_1}{10}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_1 = 15 \times 10 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 1st Object = {\pink{\sf{150 \: N}}}}}}$

• Weight of 2nd Object :

${:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 13 = \dfrac{W_2}{15}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_2 = 13 \times 15 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 2nd Object = {\purple{\sf{195 \: N}}}}}}$

• Weight of 3rd Object :

${:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 9 = \dfrac{W_3}{20}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_3 = 9 \times 20 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 3rd Object = {\pink{\sf{180 \: N}}}}}}$

• Weight of 4th Object :

${:\implies{\qquad{\sf{ Gravitational \: Field \: = \dfrac{Weight}{Mass}}}}} \\ \\ \ {:\implies{\qquad{\sf{ 3 = \dfrac{W_4}{50}}}}} \\ \\ \ {:\implies{\qquad{\sf{ W_4 = 3 \times 50 }}}} \\ \\ \ {\qquad{\textsf{ Weight of 4th Object = {\purple{\sf{150 \: N}}}}}}$

$\qquad{\rule{150pt}{1pt}}$

⚝ Comparing the Weight :

$\qquad \: {\sf{ W_1 = 150 \: N}}$

$\qquad \: {\sf{ W_2 = 195 \: N}}$

$\qquad \:{\sf{ W_3 = 180 \: N}}$

$\qquad \:{\sf{ W_4 = 150 \: N}}$

Greatest : 195 N

$\qquad{\rule{150pt}{1pt}}$

⚝ Therefore :

❝ 2nd Object has the greatest weight (i.e, 195 N) . ❞

$\\ {\underline{\color{darkblue}{\rule{300pt}{9pt}}}}$