Question

The mass of earth is 6*10^24 and its radius is 6400km. what is the mass of a man weighing 977 newton in a spring balance?

Answer 1

Solution :

➡ Given:

✏ Mass of earth = 6 × $10^{24}$ kg

✏ Radius of earth = 6400 km

✏ Weight of man = 977 N

➡ To Find:

✏ Mass of man.

➡ Concept:

✏ We know that weight force W = mg

• W denotes weight force
• m denotes mass
• g denotes gravitational acceleration

✏ So, we have to fing out gravitational acceleration of earth.

➡ Formula:

✏ Gravitational acceleration of a planet is given by

$\star \: \underline{ \boxed{ \bold{ \sf{ \pink{g = \frac{GM}{ {R}^{2} } }}}}} \: \star$

• G denotes gravitational constant
• M denotes mass of planet
• R denotes radius of planet

➡ Conversation:

✏ 6400 km = 6.4 × $10^6$ m

➡ Calculation:

$\implies \sf \: g_{e} = \frac{6.67 \times {10}^{ - 11} \times 6 \times {10}^{24} }{ {(6.4 \times {10}^{6} )}^{2} } \\ \\ \implies \sf \: g_e = \frac{40.02 \times 10}{40.96} \\ \\ \implies \sf \red{g_e = 9.77 \: m {s}^{ - 2} }$

• Mass of man :

$\implies \sf \: W = m \times g_e \\ \\ \implies \sf \: 977 = m \times 9.77 \\ \\ \implies \purple{\underline{ \boxed{ \bold{ \sf{ \orange{m = 100 \: kg}}}}}} \: \red{ \bigstar}$

Answer 2

$\large \underline{ \blue{ \boxed{ \bf \green{Required \: Answer}}}}$