Question

When a spring balance which shows a reading of 9 divisions on the Earth is taken to another planet of mass of twice of that of the Earth and radius thrice of that of the Earth, then it shows the reading of _________ division for the same body.

• A. 1
• B. 3
• C. 5
• D. 2

Answer 1

The correct option is D

2

Step 1, Given data

Reading of the spring balance = 9 divisions

Mass of the earth = m

Mass of the planet = 2m

The radius of the earth = R

The radius of the planet = 3R

Step 2, Finding the divisions on the other planet

We know,

Acceleration due to gravity $g=\frac{GM}{R^2}$

So we can write the equation for finding the acceleration due to gravity on that planet

$\frac{g_p}{g_e}=\frac{M_p}{M_e}\times {\left(\frac{R_e}{R_p}\right)}^2$

Putting all the values

$\frac{g_p}{g_e}=\frac{2m}{m}\times {\left(\frac{R}{3R}\right)}^2$

After solving

$g_p=\frac{2}{9}{g}_e$

Now we know,

Weight of a body $w=mg$

So,

$$\begin{gathered} \frac{w_p}{w_e}=\frac{g_p}{g_e} \\ Or,w_p=\frac{g_p}{g_e}{w}_e \end{gathered}$$

Now putting all the values

$w_p=\frac{2g_e}{9\times g_e}\times 9x$

After solving

$w_p=2x$

This means that the reading will be 2 divisions.

Hence the correct option is (D).