Sankalp NEET Full Test-1 Question-33 Solution

Question: 33. The mass of a planet is \frac{1}{10} th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is :

(1) 19.6 \mathrm{~m} \mathrm{~s}^{-2}

(2) 9.8 \mathrm{~m} \mathrm{~s}^{-2}

(3) 4.9 \mathrm{~m} \mathrm{~s}^{-2}

(4) 3.92 \mathrm{~m} \mathrm{~s}^{-2}

Answer: Option (4)

Explanation:

The acceleration due to gravity on a planet is given by

g = \frac{GM}{R^{2}}

Let the mass and radius of the earth be M_E and R_E respectively.

For the given planet,

M = \frac{1}{10} M_E

The diameter of the planet is half that of the earth, so its radius is also half.

R = \frac{1}{2} R_E

Acceleration due to gravity on the planet is

g' = \frac{G \left(\frac{1}{10} M_E\right)}{\left(\frac{1}{2} R_E\right)^2}

Simplifying,

g' = \frac{G M_E}{R_E^2} \times \frac{1}{10} \times 4 g' = \frac{4}{10} g_E g' = 0.4 \times 9.8 g' = 3.92 \, \mathrm{m\,s^{-2}}

Hence, the acceleration due to gravity on the planet is 3.92 \, \mathrm{m\,s^{-2}}.