Question

A body weights $700g\omega t$ on the surface of earth. How much it weigh on the surface of a planet whose mass is $1/7$ and radius is half that of the earth

• A. $200g\omega t$
• B. $400g\omega t$
• C. $50g\omega t$
• D. $300g\omega t$

Answer 1

The correct option is B

$400g\omega t$

Step 1. Given data:

1. Weight at the surface of the earth, $W$ = $700gwt$
2. Mass of the planet, $M=M/7$
3. The radius of the planet, $R=R/2$

Step 2. The formula used: Acceleration due to gravity at the surface of the planet, $g=\frac{GM}{R^2}$where, $M$ is the mass of the planet, $R$is the radius of the planet, $G$is the Gravitational constant in SI units.

Step 3: Calculate the acceleration due to gravity on the planet,

Substituting the values,

$g^{\text{'}}=\frac{G(M/7)}{{\left(R/2\right)}^2}$…………..$\left(i\right)$

$\Rightarrow g^{\text{'}}=\frac{4g}{7}$

From $\left(i\right)$, the weight of the planet is found, as

$W^{\text{'}}=mg\text{'}$$=m\left(\frac{4g}{7}\right)$ ……..$\left(ii\right)$

$\Rightarrow \frac{4}{7}\times 700gwt=400gwt$

Hence the weight of the body at the planet is $400gwt$.

The correct option is B.